"The Best Times," which NBC premieres for a six-week trial run at 8 tonight on Channel 4, isn't just a good show, it's a fine show. There haven't been a lot of fine shows lately. "Lou Grant" was a fine show. "The Cosby Show" is one. "Miami Vice" may be a great show, but you wouldn't call it a fine show. It's not even remotely ennobling; just five or six sticks of lighted dynamite that explode in gorgeous pyro-Technicolor.

But "Best Times" has a little dignity, a lot of intelligence, and a tenderness that never gets drippy and self-congratulatory, and the amazing thing about that is, it deals with high school years, a milieu that regularly brings out the worst and crassest in pop entertainments. Tonight's premiere is funny, touching and very decent. It's the kind of program you can lose yourself in. It's the kind of program you can even find yourself in.

At the stabilizing center of the series is Janet Eilber, a mature and enchanting actress playing a single mother who teaches at the high school (John F. Kennedy High) her daughter attends, and so has to balance the theoretical and the practical in raising the girl. Eilber, a lead dancer with the Martha Graham company (she has a ballerina face), is coincidentally on view in the current pay-TV premiere of "Hard to Hold," in which she had the thankless role of fawn to the preening Rick Springfield.

It would appear her particular ingratiating qualities are better suited to the intimacy of television. There's a very nice scene near the end of the premiere tonight in which she has bicycled all the way over to the house of a male teacher she fancies, bringing him a slide projector as the pretext for getting better acquainted. But when she arrives, she finds him in his bathrobe and already outfitted with female companionship. The disappointment she feels is delicately but touchingly communicated.

The script, by coproducers Seth Freeman and Michele Gallery, is constructed so that Mom can use this experience to elicit a confession out of her daughter about the boy who made a fool of her at the Potato Palace, a fast-food joint she works at in the local mall. The daughter is played by Beth Ehlers. The two actresses make a charming and believable team. Eilber in her best moments comes across as a combination of Veronica Hamel and Shelley Long. Her very best moments, that is.

Directed with a sure but gentle hand by Edward Zwick (who did the innovative "Special Bulletin"), "Best Times" divides its time fairly evenly between adults and borderline adults. Two or three story lines are kept running along, one of them semicomic and involving Jay Baker as Tony Younger, a fast-talking character obviously patterned after the ones played by the masterfully original Anthony Michael Hall in John Hughes' "Sixteen Candles" and "The Breakfast Club." Baker is no Hall. But he registers.

The other major story line finds senior Neil "Trout" Troutman (David Packer) rejecting all offers of dates so as to be true to his steady (Alexandra Powers) even though she has moved off to Indiana. But his friends egg him on and finally he accepts a blind date, so long as the date realizes this is just platonic, that he's spoken for, that nothing will come of it, and so on, and then he meets her, and it's This Real Terrific Girl.

Then guess who arrives on a visit from Indiana. The dilemma is not treated farcically. It's something that could happen. The characters in "The Best Times" deal with their problems realistically and they try to maintain a little self-esteem in the process. The problems include things like big zits, and going half the way as opposed to going all the way, but there's none of that "Grease"-"Happy Days" falsification of adolescence. Nor is it romanticized as the most exquisite torture known to humanity.

Indeed, the program is so temperate (it includes an original song, but it's not a shrieky rock tune, and there's no overt attempt to look like MTV), treats its characters with so much respect, that one well may doubt its commercial chances, especially on a Friday night when kids largely control the tube, and leading off a schedule that includes the silly "Half Nelson" and the loud "Miami Vice." The title is awkward, and arguable, and the stuff about the misunderstood gang member a little trite, but this is the kind of program a seasoned viewer might well have assumed nobody would bother to make any more.

Somebody did. And it's so fine.