it seems to me that most of the posts above are what i'll call "modifying your body" type of tips...things like build endurance, get stronger, get better contact strength...these all can help...BUT...Most of this is "unnecessary" for upper 11's and low 12's of the technical variety that we have in the PNW (your post wasn't specific as to the "type" of 5.12 climbing required)...we don't really have sustained steep climbing around here...not like say the southeast...so i'll keep my comments to the type of sport climbing you're most likely to find around here...
What you really really require to climb 5.11's and low 5.12's is technique...and this is a subtle technique that i'm talking about...the surest way to find this is to climb w/ "quiet feet"...don't just hurl your foot on to holds...place them on carefully, make sure your sole is really biting in to the hold...you want literally 90% of your weight on the footholds...
Toprope everything that is offered to you...regardless of the level...in fact don't even ask...you'll learn quicker w/ a mix of stuff that's way over your head and waaaay under your ability...but don't fall into a project trap that has been recommended above...i can't count the numbers of climbers that go out to si and beat a good 5.11+ into the ground, get it all slick and then go to a new area and get trounced by 5.10's and other 5.11's...be sure to fill in your base...if you go out and project something, MAKE SURE that you also complete other routes that are onsightable or done in a couple of go's...
As far as strength goes, you need to be able to do about 1/2 a pullup to climb 11+/12- in the PNW....