There are several ways to get the wall plumb. One way is to buy a plumb-bob, which is essentially a weighted point attached to the end of a string. Simply mark the floor where you plan to place the bottom plate, then hang the plumb-bob from the ceiling, and adjust until you find the spot on the ceiling where the point of the bob aligns with the one on the floor. If you mark each end of the wall at the ceiling in this fashion (the center, too, for good measure) you will know exactly where the top plate should go. Remember that you are marking the edge of the top and bottom plates, so you want to mark one side of your line or the other with several X’s to show which side of the line you are going to nail the plates. Make sure whichever side you mark the X’s on the floor, you mark the same side of the line on the ceiling or your new wall will be leaning quite a bit.
Another way (without a bob) is to partially nail the bottom plate (so you can pull up the nails and adjust, if necessary) to the floor. Then, take the top plate and nail a wall stud at each end. Raise the top plate to the ceiling, bending inward the studs so you can get the wall up easily. Then, slide the bottom of the studs outward along the bottom plate until the top plate is pressed to the ceiling securely, but the studs are not fully extended. Take a level measurement of the studs, sliding the top plate one way or another until level. When you’re satisfied, mark the ceiling, then fully extend the studs and nail everything together. If something should slip during the assembly, you have the marks on the ceiling to re-align everything.
And no, you do not need to remove the plaster. If your ceiling has a texture coating, might want to take off any really high pieces. Then, just make sure it’s a good, solid surface, and make sure, when you are nailing into the ceiling (and floor, too), that you are nailing into floor joists, rafters, or whatever is above the ceiling.
As an FYI, consider whether you want/need any electrical/cable TV/etc. service in the new wall before you nail and seal everything up, and as always, consult your municipality for the appropriate permits, if needed.