In productions I have done with two levels we have taped the second level in a different color on top of the first level. On the first day of blocking I talk the actors through what is taped out (i.e. "there is a spiral staircase here- you have to make 2 complete circles to get to the second level. The SR door swings both directions but the SL door only swings towards offstage.") There are ways to indicate this with tape but I find that briefly talking through it clears up a lot of potential confusion.
If you have room in the rehearsal space to tape out the second level behind the first, that could work too. (Depending on the set- some sets that might prevent the director from seeing the actors on the second level, if there are folks on the first level). It might not be a bad idea to ask your director if he/she has a preference. The actors are going to have to get used to actually having stairs when you move to the theatre no matter what, so whichever option you go with, make sure that the actors are aware of the distance they need to travel and how to get there.
I'm also at a bit of a loss as to how I can notate the blocking. I'm pretty sure the method of simply putting the second level behind the first will work well for that, I just want to be sure-what do ya'll think?
That sounds like it would work fine- you should do what makes sense for you. I also use underlining to indicate blocking on a second level or platform. "Joe x
DS" indicates that he's crossing downstage on a platform or level.