THE FIRST REAL tests in the race for the Democratic presidential nomination will come, one right after another, beginning at the end of the month. These contests won't decide the nomination; in fact, no delegates will be selected. But the results will help to shape the campaign.

* Friday morning, Sept. 30. Here in Washington, the National Education Association's board of directors will meet to vote on a presidential endorsement; a 58 percent vote is needed to win. The expected winner is former vice president Walter Mondale, who had close ties to the NEA when he was in the Senate and as a member of the NEA-endorsed Carter-Mondale ticket. The lack of suspense about the outcome--and the fact that state NEA affiliates don't have to go along--should not obscure the value of this endorsement. The NEA sent 302 delegates to the Democrats' last convention. And the association's members, spread across almost every part of America, are good campaign workers.

* Saturday morning, Oct. 1. The general board of the AFL-CIO will assemble at the Diplomat Hotel in Hollywood, Fla., to vote on its endorsement-- which Mr. Mondale is also expected to win. The scheduling of the endorsement this early was taken as an indication that union leaders had decided to back him. Other candidates are talking wistfully of preventing him from getting the two-thirds vote needed to win (the endorsement won't be final until voted by the full convention on Wednesday, but there's no doubt it will follow the general board). Labor leaders are not universally popular these days, and this endorsement might hurt a Democrat in the general election. But no Democrat wants to attack union leaders in the primaries, and the endorsement, if Mr. Mondale wins it, should do nothing but help him in the spring. The question is how much. The AFL-CIO hasn't endorsed so early before, and its 14 million members no longer automatically heed their leaders' advice. They aren't spread evenly across the country, either, and many of the early Democratic contests--in New Hampshire and the South--are in states with low union memberships. But it's still an endorsement any candidate would like to have.

* Saturday afternoon, Oct. 1. There will be a straw poll at the Maine Democratic state convention in Augusta. Mondale, Alan Cranston and Ernest Hollings have been campaigning vigorously, seeking out and talking to the 3,000 local and party officials who are eligible to vote; these are pretty much the same people who will select Maine's national convention delegates early in 1984. Failure to win or to meet some arbitrary goal in a straw poll shouldn't be taken as a sign of weakness. But the ability of a lesser-known candidate to do well in a straw poll, as Mr. Cranston did in Wisconsin in June, is evidence that he may be able to win support in a contest that counts.