There is a new edition of The Washington Post that will never smudge your fingers.

It's The Electronic Washington Post, which is now being delivered over telephone lines to home computer users who subscribe to CompuServe, a computer and information service based in Columbus, Ohio.

Since Feb. 17, CompuServe subscribers with a telephone hookup known as a modem have been able to view the electronic edition of The Post in 189 cities across the country by making a local phone call. (Users in other cities can hook up via long-distance calls.) Users -- billed on credit card account -- pay a small one-time subscription fee and then 8 1/3 cents a minute, or $5 an hour. for the amount of time they are connected. The service is available from 6 p.m. to 5 a.m. weekdays, and all day weekends and holidays.

Each evening, a separate staff of Post editors uses telephone lines to send CompuServe from 60 to 70 news, sports and financial stories from the nest morning's paper for viewing that night.

In addition, the data base from The Post available to CompuServe subscribers includes editorials and editorial commentary; movie, television, record and book reviews; a selection from the wires of the Associated Press; entertainment guides; hobby columns; and letters to the editor referring to both the printed and electronics versions of The Post. A special section on computer news also is provided.

The electronic edition of The Post also includes guides to Congress and the Reagan administration and other news and information about the federal government.

The Post's electronic edition is part of an experiment organized by the Associated Press to give its member mewspapers experience with electronic publishing. The experiment also will include research to try to determine what kinds of information home computer users are interested in and what kind of market exists for electronic publishing.

The New York Times, the Norfolk Virginain-Pilot and Ledger Star and the Columbus Dispatch also are available at this time through ComprServe. By the end of the year, eight other papers plan to join the service.

Donald E. Graham, publisher of The Post, said "We're involved with CompuServe because we want to see if we can give better service to our readers this way. We want to learn about this and other new ways of bringing the news to people.

"We hope to learn a lot through our association with CompuServe and we plan to pursue this and other experiments vigorously."

Later this year, The Post will participate in a terletext experiment sponsored by WETA (Channel 26) and New York University's Alternate Media Center. Forty terminals -- television sets equipped with decoders -- will be placed in homes in Adams-Morgan, Anacostia and Methesda, and another 10 terminals in public places. The participants will include the National Weather Service the Washington Consumer Checkbook and the District's Martin Luther King Public Library, among others.

CompuServe, a subsidiary of H & R Block Inc., also provides a computer games, electronic mail service, magazines and newsletters and personal computing services -- programming languages, a software exchange and computer file space. It has 8,542 subscribers nationwide, 426 of of whom are in the Washington area.