If you think you'd like to cruise somewhere warm this winter, get your travel agent working on it right away. Demand for cruises has skyrocketed, especially during the past 18 months. "Every ship line in the world is trying to get more lines in service," says Ken Grant, cruise editor of The Travel Agent Magazine.

Last-minute cancellations, sometimes open up a berth on a Christmas cruise, but most of them are already wait-listed. The first week in Janurary, however, can be slower than the rest of the winter season. For the pick of the trips, you should be thinking now about winter, 1981.

One reason for cruises' popularity is thier fasted price. You know in advance exactly what your vacation will cost. Liquor, gifts and tips (about 5 percent) are the only expenses not included in the basic package.

The average cost per day, in a two-person cabin with porthole, is about $125. More expensive accommodations run $160 to $175, and cheap ones, around $80. It generally costs 50 to 75 percent more for one person booking in a two-person room.

These prices represent an increase over last year of 10 to 25 percent, depending on the cruise. Some lines have a fuel surcharge of $7.50 to $10 per day.

A variety of discounts available, according to Else and Bennet Daniels, authors of "Vacation at Sea" (Sovereign Books: $12.95 or $5.95 in soft cover). They include 10 percent cuts for people over 65; 7.5 percent reductions in September and October, and 15 percent in March and April; 20 percent discounts on some cabins for people aged 15 to 25; and 10 percent discounts for four people sharing a double room.

On older ships therre are cheaper rooms without a private bath. On all cruises, cabins cost less on the lower decks and inside of the ship. Russian ships are $100 to $200 cheaper, and tipping is prohibited.

Special air-sea packages let you fly to your port of departure for as little as half the regular fare. Longer cruises may even include a free flight. For example, the Sitmar Cruises offers free round-trip air fares from 130 cities for passengers on all 20 of its two-week, trans-Panana Canal or Caribbean Cruises.

The most popular ports of departure are New York, Los Angeles, San Francisco, Montreal and Miami-Fort Lauderdale. A limited number of cruises also leave from such cities as Boston, Philadelphia, the District, Norfolk, Charlotte, Tampa, New Orleans and Tacoma. Starting from the south rather than from the North gives you more days in the sun.

Top lines for the monied set are the Viking Lines, Norwegian American, Cunard and Marriott's Sunlines, Else Daniels told my associate, Dedra Hauser. French ships are known for their cuisine, Scandinavian ships for their spotlessness, modern art and efficiency, and Italian ships for their convivality.

Many cruises are tailored to special-interest groups, offering lectures on photography, backgammon tournaments, cooking classes and so on. Travel agents have folders on some of cruises; you'll also find them advertised in special-interest publicatons.

Some comparison costs, for one-week trips from San Juan, Puerto Rico (not including air fare): $445 to $950 per person on Costa Lines Amrikanis, and $710 to $1,340 on its Benae or Daphne; $340 to $880 on Chandris Lines' Britainis; $674 to $1,195 on Cunard's cunard Countess; $595 to $1,175 on Hellenic Mediterranean's Aquarius.

Freighter cruises generally attract retired people, because their itineraries are so uncertain. But their limited number of passenger berths are so popular that you have to book about two years advance. Typically, there are 8 to 12 passengers per ship, and no entertainment except the house-party atmosphere that the travelers themselves create.

Sample prices: $1,900 per person on Moore McCormack's 30-day trips, New York to Brazil; and $2,350 for 40-day trips to Brazil and Uruguay. Trips in the Pacific run $50 to $60 a day.