The programmers room can be reached two ways, the first is when Chrono first goes to the fair and meets his friend Lucca(the inventor) when he is supposed to go onto the teleporter on the left, go on the one to the right and push 'A'(I think, you have to push one of the 4 buttons any way). Doing this will take you to the last boss, its impossible to beat it at level 1 with just Chrono(it might be possible if you got Chrono up to a high level(99?)and did New Game+). However, you can do this later in the game if you come back to the same spot, but I'm pretty sure at one point you can't do that anymore.Anyway, kill all three forms of Lavos and you win the ending with the Programmers. All it is is that you go to the end of Time and can enter the pillars of light which will send you to different points in the game. Talking to the monsters will let you see what the programmers would say.
The other point is when you meet Lavos and you are supposed to be killed by him, if you kill him and the other two forms, you will also get the ending.