Coast Guardsmen boarded a Soviet trawler, 80 miles southwest of Martha's Vineyard yesterday and began enforcing the nation's 200-mile fishing limit by writing the Soviets a warning that they were violating the law.

It was the first such boarding on the morning the law look effect.

At the same time, a small armada of Spanish fishing vessels left the Atlantic for New York Harbor wit their nets stowed because diplomatic and conressional red tape has left their country temporarily unable to fish in U.S. waters.

And off the Pacific Northwest, where all foreign fishing except for tuna is suspended until June 1, no foreign fishermen were in sight.

From the rich fishing grounds off New England to the even richer grounds off Alaska, the Coast Guard began trying to enforce the new rules laid down to protect the catches American fishermen have sought to reserve to themselves.

Some 116 foreign vessels were reported off the East Coast yesterday - 68 of them Russian.

So far, only seven nations have agreements in force allowing their vessels to buy permits and fish in the U.S. zone - Canada, Poland, the Soviet Union, Romania, Bulgaria, East Germany and Taiwan.

Fisherman from four other fishing powers - Japan, Spain, the eight maritime nations of the European Common Market and South Korea - are waiting for Congress to approve agreements their nations have signed.