Take all information as if your standing over the bike , so as not to cause confusion. the left hand cup ( non drive side) is better known as the "guide cup" at first you must only thread it in half way.
Then begin installing the drive side, by installing the non drive side first you give the right side a guide so as not to cross thread the drive side. Install the drive side tight to the frame, as tight as
you can manage then if you feel it needed get a cheater bar and give it that little extra. after the drive side is snug as can be finish installing the non drive side, so not over tighten if you have a plastic cup.
Once this is all complete assemble the cranks onto the bike, tighten them to torque speck by your manufactures recommendation. grab both cranks and rock them to see if there is play, if not go ride it for a few minutes.
Then re check for play, hopefully this has helped.
A really good cleaner use white lightning able to be purchase in most bike shops. Also known as Clean streak or metal prep. make sure to remove all residue with a rag after doing this.
If you find yourself unable to complete this task you might seek professional help as to not damage your bike. The bottom bracket is the heart of the bike if you damage it she wont run.
good luck from Canada.
Ben.