Su.Ki. and Clinton gave the usual interpretation. Here some variations. "Go up the stairs TO the right." = Go up the stairs which are to the right. "Go up the stairs ON the right." = Go up the stairs which are on the right. "Go up the stairs, THEN GO/TURN right." = Go up the (only) stairs, then at the top, go right. "Go up the stairs, THEN right." = Go up the (only) stairs, then at the top, go right.

I agree with Clinton. If the speaker had meant to say "Go up the stairs and turn right", that's what they would have said. This would be two separate instructions: first go up the stairs, and then turn right. I would understand your sentence to mean "Go up the stairs [which are] on the right". There are some stairs on the right, and you should go up them. The only way that you might interpret this as 'first go up the stairs and then turn right' would be if the staircase split in some way. For example, if there are some stairs and then a landing where the staircase divided into two, with one flight of stairs going left and one going right. But then, it would amount to the same instruction: you need to go up the stairs which are on the right ( as opposed to the stairs which are on the left).

Thank you teachers, all of you teacher's answers helped me a lot.

Yes, exactly.

It means that the stairs you are looking for are on the right. What you will find at the top of the stairs is not specified here.