SEARCHING for family roots in Ireland (one in 10 Americans has them)--or searching for family roots anywhere, for that matter--is a treasure hunt of enormous satisfaction. Every search is unique, yet the ways and means are common to all. It's probably the most rewarding kind of detective work, because the mystery being unraveled is your own.

The quest for a past sometimes ends in the present with the biggest find of all: proving kinship with living relatives in the old country. In Ireland, that's no mean prize, given the legendary hospitality of the people. And the likelihood of it actually occurring is heightened by a number of factors.

In the first place, emigration from Ireland to America is a relatively recent phenomenon, with the biggest waves touched off by the great potato famines of 1845-48 and followed for the next half-century or so. What that means in practical terms is that your research is limited to a handful of generations, and thus made easier.

Also, the Irish are possibly the most rooted people in western Europe, with near-mystical ties to the land--the specific hills, fields, communities--of their birth and heritage. There are solid reasons for this. Celtic Ireland was a loose federation of some 150 tuaths, or clans, each ruled by a hereditary chieftain. Although they were sometimes nominally united under the High King of Ireland, in reality the Irish people never accepted the principle of centralized authority, as the invading Normans learned painfully in the 12th century and as did the English in later times. The passionate devotion of the Irish to their own very specific localities has endured through the centuries. Look at an early map showing the distribution of noble families in the 15th century, then check 20th-century telephone books if you want proof: large numbers of their descendants are still living in the same locales. Irish surnames are intrinsically linked with particular places.

Of course, it is nearly pointless to go off in search of "John Burke who left Ireland for America around 1850." A check of emigrant passenger lists of that period probably would turn up dozens, if not hundreds, of people meeting those qualifications.

The search for Irish roots is really a two-part endeavor, here and there. First, it is critically important to find out as much as possible about your family's history and ties on this side of the Atlantic. Learn, if you can, the full name of your emigrant ancestor, the family background (rich or poor, farmer or merchant, etc.) and his/her religion. It is also a big advantage if you can learn from which part of the country your ancestors came, because surnames, though rooted to the land, can be widely dispersed. Pinpoint the county as well as the village if you can, because place names are duplicated. My own search took a costly detour to Whitegate, County Cork, when I really wanted to be in Whitegate, County Clare, for example.

The way to go about this is to learn from older family members here as much as possible about their recollections of family ties, and to peruse with vigor the informal family archives--old letters, diaries, perhaps a family Bible, photographs, and less-obvious clues such as regimental buttons on old jackets. Discard nothing. People are inclined to ignore little leads, such as license plates on cars in old photos. Also, remember that what are non-clues to you may turn out to be valuable leads to the trained searchers you may later enlist to help you. For example, to an American eye, all thatched cottages look alike, so that old photo doesn't help very much. But to an Irish eye, the same photo can pinpoint the vernacular architecture of a very specific locale.

Record your conversations with family members and other sources, if possible. Things that seemed too insignificant in the first telling to take note of could in fact be priceless clues that otherwise may be lost. Being able to replay the conversations as the research continues is invaluable.

Rake your own memory for remarks or conversations from earlier days at home. A friend of mine put six generations of Nolans together by recalling a casual exchange between his parents some 25 years ago. The topic was a dispute with a neighbor. My friend's mother, he remembered, said to his father, "Why don't you sue him, Rex?" "I couldn't do that, Constance," he answered. "Sure and he's kind of a relation."

Always work backward from known ancestors, never, never trying to hook up your line by working forward from some well-known or historic individual. You'll get trapped and misled if you try, and anyway the search for prestigious ancestry has lost the cachet it had for the social climbers of the 19th century. It's much more fun to discover the quirks, skeletons and even scandals in your own family closet than to try to establish a purple tint to your all-American red blood (though in Ireland those 150 original kingdoms give nearly everyone a shot at some royal connection.) The essential thing is to discover who your ancestors were, not how important they were.

The National Archives on Constitution Avenue has all kinds of records--census data, war records, vital statistics--to help you trace your family back to its arrival in the United States, and it gets some 2,500 requests per week to research facts in family histories.

Publications such as the American Genealogical Index by Fremont Rider and Genealogical Research, Methods and Sources, published by the American Society of Genealogists, are helpful and generally available in libraries.

For how-to-search books, family tree charts and all manner of tools for the amateur genealogist, head for the Hearthstone Bookshop, 108 S. Columbus St. in Alexandria (549-8211). Their catalogue is available by mail for $1.

Then, once you've established the identity of your emigrant ancestor, the Irish part of the hunt begins, with the help of records on both central and local levels.

Because Irish records have suffered much in the course of a troubled history--particularly in the last three centuries--the country's files cannot match those of other European countries such as England and France. Two particularly disastrous losses were the destruction of the Record Tower in Dublin Castle in 1710 and the burning of the Public Office in the Four Courts of Dublin during the Civil War in 1922.

Nevertheless, there's a surprisingly strong interlocking network of information sources--libraries, record offices, archives, church registers, graveyards and a wealth of local knowledge and traditions.

Many important sources are centralized in Dublin City. The General Civil Registration of births, marriages and deaths (known in genealogical circles as Hatched, Matched and Dispatched Files) date from 1864 and are housed at the office of the Registrar General in the Customs House.

The National Library on Kildare Street has endless collections of directories, family and local histories, topographical works, newspapers and manuscript collections (deeds, letters, etc.) relating to many Irish families.

The Registry of Deeds on Henrietta Street houses records from 1708 onwards. Deeds are a valuable source of tracing the pre-emigration history of a first-generation American (your Irish immigrant ancestor). Sometimes a father naming all his children in a deed might mention a son "gone to America" with a provision including him in the deed "if he returns from America" and excluding him if he doesn't.

Despite the damage it suffered in 1922, the Public Records Office in the Four Courts still houses valuable records, especially its collection of wills and Tithe Applotment Books containing the first Valuation Office Records and the names of people whose holdings were subject to tithes during the first half of the last century.

The Genealogical Office in Dublin Castle also has lots of material, but it is more likely to be of use to people who already have made considerable progress and is not the place to start cold.

On the local level, parochial registrars in the custody of parish priests all over Ireland are goldmines.

There are many ways to go about tapping these sources. You can do it yourself, which is time-consuming and requires familiarity with such quirks in the Irish records system as, for example, the impact of the 1907 introduction of old-age pensions in Ireland. Since birth records only existed back to 1864, making it impossible to disprove their claims, any number of people added 20-25 years to their ages in the 1911 census, thus qualifying for immediate pensions. Anomalies like this drive you batty if you can't explain them.

A veritable fountainhead for amateur genealogists in Ireland is Heraldic Artists Ltd.'s Genealogy Bookshop at 3 Nassau St., Dublin 2; (01) 762391. Two of its most useful publications are Handbook on Irish Genealogy and Irish Genealogy: A Record Finder. The first is a basic primer for people of Irish descent to get personally involved in their backward journeys; the second contains 2,000 precise references to existing Irish genealogical source records and pointed advice from leading genealogical experts on reliable documentary approaches to ancestor hunting. Both are available by mail at $9.00 and $15.50 respectively for surface mail, $12.50 and $19.50 airmail. Ask them to enclose a catalogue of their other publications as well.

The second option is to let someone else do the work. The Genealogical Office in Dublin Castle will undertake searches of its own records and those of the other mentioned sources for a fee. Likewise, the Hibernian Research Co. Ltd., Windsor House, 22 Windsor Rd., Rathmines, Dublin 6, will conduct a five-hour search and give you a full written report for $65. Further research from this group of full-time professional genealogists may be commissioned at an hourly rate plus expenses once the report is in hand.

The third option is in many ways the most appealing, for it combines the other two and promises you a relaxed and rewarding Irish vacation as well. These are Irish Heritage vacation packages, available thanks to some imaginative planning by Shannon Development Co. (a government agency charged with economic development in the west of Ireland, including tourism) and Aer Lingus (the Irish national airline) with the assistance of the Irish Tourist Board.

They were mindful that some 20 million-plus Americans have Irish roots. (President Reagan's family was traced recently to Ballyporeen, a little town in County Tipperary.) They also detected a groundswell of interest in finding one's origins that occurred throughout the entire American populace after the 1976 Bicentennial and especially as a result of the broadcast of Alex Haley's celebrated "Roots" television mini-series.

The happy result was a series of Heritage Packages, which offer an unstructured Irish vacation as well as a number combining Irish vacations with the assistance of qualified genealogists. Actual roots research is available as options on the program, both inthis country and in Ireland. Roots research in Irish family history in the United States costs $75-$100 through the program. Roots research in Ireland costs $110-$135 and includes a personal briefing by a member of the research group when the traveler arrives in Shannon.

Tour participants get a rental car with unlimited mileage, vouchers for accommodations at either hotels or guesthouses throughout Ireland, and a listing of more than 100 local historians throughout the country who will help them at the local level for a consulation fee of about $14. (A voucher for one free consulation is included in the package, as well as a special Ireland of the Clans Guide and a map showing places associated with their clan.

Full details on the Heritage programs are available from Aer Lingus (800-223-6537) or Shannon Development, 590 Fifth Ave., New York, N.Y. 10036 (212-581-2081).

For an informative capsulization on tracing Irish roots, contact the Irish Tourist Board, 590 Fifth Ave., New York, N.Y. 10036 (212-869-5500) and ask them to send a copy of Information Sheet Number 8: Tracing Your Ancestors. It's free.