NBC and the Olympics made it official yesterday, formalizing a $300 million contract that gives the network the television rights to the 1988 Summer Games in South Korea.

The contract was signed by the network and the Seoul Olympic Organizing Committee in a brief ceremony at International Olympic Committee headquarters in Lausanne, Switzerland. NBC last did the Olympics in 1964 from Tokyo, although it had the contract for the 1980 Games, which were boycotted by the United States.

The network said it expects to televise about 180 hours from Seoul, 75 percent of it live. Many events will be held in the morning in Korea, which, with a 14-hour time difference, will put them in prime evening time in the United States.

The fee is half the $600 million organizers had hoped for and less than the estimated $309 million ABC paid for the 1988 Winter Games in Calgary, Canada.

Commissioner Peter Ueberroth has declared baseball's playing fields, dugouts, clubhouses and related facilities and areas off-limits to all but essential personnel.

The directive, effective immediately, applies to spring training, regular season and playoffs. It bars "friends, business associates, agents, attorneys, equipment salesmen or other vendors, unauthorized doctors or therapists, etc.," with the objective to "remove distracting elements from the game."

The commissioner also said the clubs have been asked to apply more stringent security in hotels during road trips.

Ueberroth had promised to tighten clubhouse security when he announced last month his decision concerning players involved in the Pittsburgh drug trials.

Yesterday, he commended the players who went along with his alternatives to suspension, and added: "In response to certain press reports, I want to clarify that it was not my intention to suggest to anyone, nor should anyone have concluded from my decision, that Keith Hernandez or any of the other following players included in the first most serious grouping -- Joaquin Andujar, Dale Berra, Enos Cabell, Jeff Leonard, Dave Parker and Lonnie Smith -- was in any sense a drug dealer, pusher or otherwise engaged in any sort of drug trafficking." . . .

The handshake that broke the little finger on Texas Rangers knuckleballer Charlie Hough's pitching hand was no ordinary handshake.

Knocked out of his opening night starting assignment against Toronto April 8, the veteran right-hander will have a steel pin implanted into the finger today.

Hough says he was injured as he left a party Monday evening and shook hands with an unnamed friend -- then the two locked fingers and continued the maneuver in a semi-high-five.

Next day, it hurt. X-rays showed a break below the lower knuckle. COLLEGES

University of Texas Athletic Director DeLoss Dodds says a law firm has been hired by the school to "get to the bottom of any alleged violations" of NCAA rules in the UT football program. Dodds said the move is in response to reports in The Dallas Morning News and Austin American-Statesman alleging breaches by players, coaches and boosters . . .

Cherry Bowl officials, citing a steep drop in attendance for the second annual postseason football game in Pontiac, Mich. -- Maryland versus Syracuse -- have dismissed Frank (Muddy) Waters as executive director and Michael Mills as marketing director. The 1984 Cherry Bowl, Michigan State-Army, drew 70,000 to the 80,000-seat Silverdome. Last December's game drew 22,580 despite pregame sales of 51,858 tickets . . .

Elvin Hayes may be a leading candidate to coach the University of Houston, The Houston Post reported about the Houston alumnus whose Bullets number hangs retired in Capital Centre. Houston already has talked to Iowa's George Raveling, who may be named the coach at Southern Cal today, and Navy's Paul Evans, who is bound for Pitt . . .

Navy has begun spring football practice and selected its 1986 captains: quarterback Bill Byrne of Pacifica, Calif., and linebacker Vince McBeth of Camden, Ark.