With the confidence of youth, many student-age travelers set off for a summer in Europe with only a sketchy itinerary and often no hotel reservations. This can be an agreeable and inexpensive way to travel, either alone or with a friend. And it certainly makes for more of an adventure than taking a guided tour.

But even the footloose American traveler can profit from good advice and friendly help in finding low-cost transportation and suitable lodging within the limits of a tight budget. Such assistance, directed specifically to student-age travelers (high school to post-graduate), is available to Europe-bound travelers, both before they go and after they have crossed the Atlantic.

Apprehensive parents, watching their offspring embark on a first trip abroad, may take comfort in knowing that European countries are accustomed to welcoming students from around the world and treating them well. One industry study estimates about 750,000 U.S. students go abroad every year.

Among the places student travelers can go for help:

* "Let's Go" guides: Any young first-time traveler to Europe should consider buying a copy of "Let's Go: The Budget Guide to Europe" ($9.95 paper), which is updated annually by the publisher, Harvard Student Agencies. It is written for students by other students who travel on a shoestring to research the book. It is the best student guide to budget travel on the market.

Other books in the "Let's Go" series include guides to "Britain & Ireland"; "France"; "Spain, Portugal & Morocco"; "Italy"; "Greece"; "Israel & Egypt"; "Mexico"; "USA"; and "California & the Pacific Northwest." They can be found in many larger bookstores.

One of the series' most valuable features is a city-by-city list of budget accommodations -- some catering only to student-age travelers. The listings include youth hostels, private dormitory hotels, on-campus dormitories, bed-and-breakfast lodgings, inexpensive hotels and convenient-to-reach campgrounds.

The guides also describe bargains available only to the young, including budget "BIJ" (or "B.I.G.E.") train tickets for travelers under 26 in Europe. The tickets come with restrictions -- for use only on certain trains or for limited hours of travel -- but they can reduce a second-class fare by up to 50 percent. These tickets are especially useful for travelers who are not going by train frequently enough to make buying a Eurailpass worthwhile.

Editor of next year's "Let's Go: Europe 1986" guide is Scott Campbell, 22, who just graduated from Harvard as a psychology and art major. He went to Europe alone four years ago, at the age of 18, and has returned every summer since, always on a student budget. Did he encounter any problems that first time abroad?

"Nothing was a problem," he says. "It was an adventure."

* Let's Go Travel Services: Another Harvard Student Agencies program, the Let's Go Travel Services is a student-run travel agency specializing in low-cost travel for student-age clients all over the country. The office offers both walk-in and mail-order service.

The agency does a big business in issuing (for $8) the International Student Identity Card, which tends to be recognized more readily abroad than a student's high school or college I.D. card. It is invaluable for obtaining reduced admissions to museums and tourist attractions and for buying reduced-price bus and train tickets. About 6,000 travelers purchased the cards from Let's Go last year.

Also available are youth hostel memberships, for reduced rates at youth hostels abroad; Eurail and BritRail youth passes, which must be purchased outside Europe; and low-cost charter flights to Europe.

Let's Go promises a "speedy turn-around" for any mail applications for the I.D. and youth hostel membership cards and for rail passes. "We have to, because of our market," says this year's manager, Ann von Germeten, a Harvard senior. "Students never plan ahead."

The agency's small student staff generally is well-traveled, so they can answer questions in the office or by phone. Says von Germeten: "People come in and say, 'I'm going to Europe.' And then there's a pause before they ask, 'What am I going to do?' They don't know the first thing."

For more information: Let's Go Travel Services, Harvard Student Agencies Inc., Thayer Hall-B, Harvard University, Cambridge, Mass. 02138, (617) 495-9649.

* Council on International Educational Exchange: A nonprofit organization, CIEE (as it is known) assists students interested in study or work programs in Europe. The organization also issues the International Student Identity Card and European rail passes, and it offers charter flights to Europe.

Staff members in the Council Travel Services office are available to answer questions on budget travel. For a $1 mailing fee, travelers can obtain a 64-page booklet, "1985 Student Travel Catalog," which contains advice on planning a trip abroad. It includes details on low-cost student accommodations.

For more information: CIEE, 205 E. 42nd St., New York, N.Y. 10017, (212) 661-1414.

* National tourism offices: Most European countries have a tourism office in New York City, and several offer special brochures or other informational assistance to student-age travelers:

The British Tourist Authority is staffed with a youth travel executive, June Kear. She can answer questions about student travel in Britain and has available special booklets on youth accommodations, including inexpensive hotels and college dormitories, and other travel tips. For example, at some campgrounds, she says, young travelers without tents can rent trailers by the night very inexpensively. For more information: BTA, 40 W. 57th St., New York, N.Y. 10019, (212) 581-4700.

The Netherlands Board of Tourism similarly offers a 24-page booklet, "Holland, a Young and Lively Country," written specifically for young travelers. It cites a number of low-cost accommodations in Amsterdam and other cities and towns (with addresses). And it provides a practical list of "useful addresses," such as public baths (if your budget hotel has no tub or shower facilities) and where to go (the Dutch are very realistic) for treatment of sexually transmitted diseases. For information: NBT, 576 Fifth Ave., New York, N.Y. 10036, (212) 245-5320.

The French Government Tourist Office can provide information on such organizations as the Accueil des Jeunes en France (AJF), a central accommodations booking office in Paris, which has 8,000 beds available for students in the summer in youth hostels, campus dorms and tourist hotels. For more information: FGTO, 610 Fifth Ave., New York, N.Y. 10020-2493, (212) 757-1125.

* Tourist offices abroad: Throughout Europe, young travelers can turn for help to tourist offices in most cities and even in many villages. These offices often can provide valuable services not normally available from American tourism offices.

In addition to usually having someone around who speaks English, most will be able to provide lists of local student or other budget lodgings, and many (for a fee of about $1 or $2) will phone ahead to make a reservation.

But young travelers should use common sense, says "Let's Go" editor Scott Campbell, and plan to arrive in any new place well before the local tourism office closes.

EXCESS BAGGAGE: A point to consider for American travelers (student or nonstudent) who plan to buy their way through Europe this summer: The cost can be quite high to check luggage that exceeds the free-baggage allowance permitted by the airlines on international flights. An overweight suitcase, or an extra suitcase, could cost you $60 to $80 or more to take home.

On the other hand, the amount of baggage you are allowed to take free on transatlantic flights is substantial. So chances are you would have to stuff large suitcases full of heavy objects to face an excess-baggage charge.

Free allowances vary by airline, but generally you are permitted to check two pieces of luggage (per person), not to exceed 70 pounds or 32 kilograms each. The total measurement of each piece (total of height, length and width) should not exceed 62 inches. A third piece may be hand carried, and it should not exceed 70 pounds or 45 inches.

Among the variations on this formula: On Pan Am and other airlines, coach-class passengers are permitted one bag at 62 inches and one at 55 inches. On TWA, the weight limit for checked luggage for first, business and coach classes is 62 pounds. And no bag exceeding 100 pounds will be accepted.

A standard-size suitcase, the kind you are apt to carry on a vacation to Europe, probably will weigh no more than 30 to 40 pounds when packed neatly with clothing, and it will easily meet the measurements requirement. That gives you plenty of leeway to stuff in new purchases.

One complication is that these allowances are for transatlantic flights. Within Europe, however, there is generally a 44-pound limit on each piece of luggage in coach class. So you might want to save any heavy shopping for the last stop before your flight home.

Airlines tend to be strict on excess-baggage charges when planes are full and less concerned when they are flying with a lot of empty seats. This summer, because of the record number of Americans going abroad, expect full planes and carefully weighed luggage.

FESTIVAL TICKETS: U.S. travelers to Britain can now get detailed information and make reservations before leaving home for 15 major arts festivals that take place there each year.

Among the most famous is the Edinburgh International Festival, Aug. 11-31. This year the theme is French (French opera, theater, music and dance), celebrating a nearly 1,000-year-old link between Scotland and France.

Reservations for this and other festivals can be booked through Edwards & Edwards, a New York ticket agency. Edwards & Edwards is representing the British Arts Festivals Association under an arrangement initiated by the British Tourist Authority.

Other events include the Three Choirs Festival, Aug. 17-23, at Hereford, near the Welsh border, and the Windsor Festival, Sept. 16 to Oct. 2, during which concerts and lectures are held at Windsor Castle and Eton College.

For a listing of "British Arts Festivals 1985," contact the British Tourist Authority, 40 W. 57th St., New York, N.Y. 10019, (212) 581-4700. For seat reservations: Edwards & Edwards, (800) 223-6108 or (212) 944-0290.

ANCIENT ISRAEL: Harvard University's Semitic Museum has organized a special two-week archeological tour of Israel this fall, and among the guides will be some of the archeologists who have dug at important new sites in the past two decades.

"Hearing the excavator tell of his or her discoveries is like reading a good detective story," says a museum spokesperson. Representing the museum on the tour are Gary Pratico and Nitza Rosovsky, assistant curators. Rosovsky, a native of Jerusalem, is author of "Jerusalemwalks."

On the itinerary are sites spanning 4,000 years, from the Early Bronze Age to the Crusades. They include Jerusalem, Tel Dan, Gamla, Belvoir, Megiddo, Masada, Caesarea, Herodion and Jericho.

The tour, Oct. 23 to Nov. 6, is aimed at travelers with no archeological experience. The cost is $1,900 per person (double occupancy), which includes round-trip air fare from Boston or New York; 13 nights' accommodation in four- and five-star hotels; most meals; and a $250 tax-deductible donation to the museum.

For information and reservations: TOURS/Harvard Semitic Museum, 6 Divinity Ave., Cambridge, Mass. 02138, (617) 495-3123.