International Business Machines Corp., the world's largest computer manufacturer, made its long-awaited entry today into the rapidly growing personal-computer market.

The computer will go on sale in October. Sears, Roebuck & Co., the giant Chicago-based retailer, will sell the IBM computers at new specialty "business machine" stores the company will open this fall in Boston, Chicago and Dallas. IBM said that ComputerLand dealers and its own product centers also will sell the new computer.

Analysts said the new IBM models will present no immediate threat to the thriving, well-established names in the personal-computer field: Apple, Tandy (Radio Shack) and Commodore.

"Instead of coming in with a machine that would be a half-step behind the industry, IBM has shown us where the market will be a year or two from now," said Sanford Garrett, vice president and analyst for the brokerage firm Paine Webber Inc.

The personal-computer market has been expanding at an astronomical pace of about 100 percent a year for the last few years, and similar growth is expected through 1982 or 1983. Manufacturers now are shipping about 80,000 units a month, and revenues average between $200 million and $250 million.

Personal computers were originally the playtoy of the hobbyist but now are used widely in schools, small businesses and in the home. With the proper instructions (called programs or software) and optional equipment, the computers can be used to write and edit letters, track stock portfolios or make charts and tables. The IBM computer, for example, will allow an owner to plug in paddles or joysticks to play computer games similar to those in bars and amusement arcades.

Although the new IBM personal computer apparently has no major technological breakthroughs, it is the fastest and most powerful machine of its type, analysts said. But like all new computers, there is a limited amount of programming available for the IBM machine. Programs tell the computer what to do.

But as the months go on, IBM itself, as well as other companies and individuals, will write programs for the IBM personal computer that will enable the machine to perform all sorts of tasks. The Apple II computer, for example, has been on the market for more than three years, and hundreds of programs are now available that will perform tasks such as payroll accounting for a small company, household budgets, stock portfolio tracking and the like.

IBM has set up a personal- computer software publishing department that will accept programs from individuals and companies and, if they are approved, will publish them.

A few programs for the IBM personal computer will be ready when the machine goes on sale in the fall. IBM Vice President C.B. Rogers Jr. told reporters this morning that available programs will include the EasyWriter program for preparation of letters and manuscripts; the VisiCalc financial analysis program; and general ledger, accounts-payable and accounts-receivable programs.

The barebones model will retail for $1,565, IBM said. It can be used with a home television set. The most elaborate system will cost about $6,000. But the average system -- which probably will include a printer, auxiliary storage diskettes and a display -- will cost in the range of $3,000 to $4,000.

That puts the price in the upper end of the personal-computer market. But the IBM model is faster and more powerful than existing personal computers, and availability of a wide variety of programs in a year or so will make it a more desirable system than most in use now.

Other manufacturers, however, can be expected to produce machines that use the same 16-bit microprocessor that is at the core of the IBM unit. Personal computers now use 8-bit microprocessors.

Garrett of Paine Webber said the size of the microprocessor determines the speed and amount of information a computer can handle. "It's like having one faucet with a half-inch tube connected to it and another with a quarter-inch tube. You can get more water from the faucet with a half-inch tube when the spigot is wide open." CAPTION: Picture, Complete IBM personal computer system shown here is intended to sell for $4385. AP