Don't worry about letting your fingers do the walking. Just make sure they do the dialing. For travelers heading abroad, that's the money-saving message from Alexander Graham Bell's medium.

As of last month, when Saudi Arabia was added to the list, telephone callers are able to direct-dial any number in the United State from 41 other countries and territories. There are several good reasons to remember this piece of news. One is that direct-dialing means that the phone company's price to call home from, for example, England is now less than $1.25 a minute - or, to put it generally, from anywhere that has the system it's 25 percent to 50 percent less than it costs to make an operator-assisted call.

Direct-dialing sometimes is also the only way to get through without a lengty wait and much frustration. Particularly in Europe at night and over weekends and holidays, reaching an international operator is likely to be a job since odd-hour staffing is expensive and therefore limited. And direct-dialing has other claims to fame.

In Europe and some other parts of the world, many hotel phones now have built-in timers and guests are billed for each "unit" used, at rates set by the hotels over and above those billed by the phone company. This has become a four-star travel trap.

Hotel-surcharge horror stories have been flooding in for about four years now, notably from Germany, France, Switzerland, Brazil and Argentina. One recent and not-so-rare one come from an American businessman who found out after the fact that his Bavarian hotel had marked up calls almost 300 percent. The topper was that not only did he wind up paying several dollars for some local calls but, after a five-minute conversation to the United States, discovered that his total phone bill came to more than the overnight price of his first-class room.

One way to beat the system is, of course, to cut out calling entirely. Not so strangely, this technique isn't all popular with telephone companies. The American Telephone and Telegraph Co's international division therefore has been out collaring all the hoteliers it can lay hands on to persuade them that telephones belong in the "services" column, along with heat and elavators, not in the "money-makers" section with a bars and breakfasts.

To sweeten the pot, AT&T has offered to pay for some advertising about "good news" hotels such as those in Ireland, Israel and Portugal that have signed up for what's called "Teleplan," which is an agreement to reduce or eliminate surcharges on calls to the United States for which charges are reversed or billed to a credit card.

Even where Teleplan is not in force, calling collect or using a credit card (available free from most local telephone company business offices) does bypass the hotel's meter, according to AT&T. It may not, however, eliminate other still substantial charges.

For just such expensive reasons, direct-dialing, which is now possible from a lengthening list of hotel-room phones, is surfacing as the best possible way around that kind of unmetered surcharge problem. Nonetheless, in many areas, there's a wasteful way to call and there is a saver's system.

A wasteful way would be to follow in the footsteps of a recent visitor to Geneva who ran up a $90 bill for a direct-dial call to Washington. The hotel's meter was running (direct dialing does not eliminate the meter, AT&T says) so part of the price was the metered surcharge. An equally sizable chunk of the bill, however, represented fallout from the falling dollar. The same call would have been roughly $30 had it come from Washington. Because many international telephone rates were set some years ago, what once was, for instance, a $6.75, three-minute, station-to-station call between the United States and Germany - without any surcharge added.

Such exchange differences, and the meter, are the reasons direct-dialing is only part of the how-to-beat-the-system story. The rest has to do with the fact that in most of the countries where the surcharge bite is biggest (Europe and Japan), three-minute-minimum rules no longer apply and you can make one-minute international calls.

Where the country but not the room phone is set up for direct-dialing, where there is no minute rate, the answer is to place the call from one of many "telephone centers" that abroad are usually installed in major post offices, airports and railway stations. There, operators will place your call for you at direct-dial rates (ordinary coin phones won't work in many places because they're operated by a single slung rather than coins, or because so many coins are needed, the mechanism to connect with international numbers has been deemed impartical)

As in the United States, off-peak calling hours are cheeper than peak calling hours, even for direct-dialing. In Europe and the Pacific, for example, rates are lowest, after 10 p.m. and until 6 or 8 the next morning and on Sundays.