I had the same problems when I installed iOS8. Frankly, it was disgraceful. Safari crashed so often that I had to resort to my PC to log onto this community to try to find possible solutions.
I ended up getting onto the Apple support page and doing the live chat thing. I had already done a full system reset which made no difference. Being out of warranty of course, I had to tick the box that indicated that I thought there was a special reason I shouldn't have to pay for support! Anyway, long story short, apart from suggesting that I do a full system wipe and restore from an iTunes connection to my PC, they couldn't offer anything useful. Let them know how cheesed off I was with their stupid update and was told there was no way possible to revert to iOS7 (which of course there may well be).
I turned my iPad2 off completely and put it away, had to do that, otherwise it was going to learn how to fly!
Later that day I turned it on and the performance seemed to have gotten better. Hmmmm, I think to myself..... that seemed to help!?
So I then turned it off again, waited a few minutes, and turned it on again. More improvement.
Have now done that several more times, and at last it seems that I am getting back to something close to iOS7 levels of performance.
I had held off doing the iOS8.02 fix, but have now done that now, it only took a few minutes, and things still seem to be running fine. I also did the "pinch screen in safari" solution mentioned earlier in this thread, not sure if it made a difference or not.
So give the old shut down and reboot multiple times solution a try, everyone. It cant hurt, and in my case has got things pretty much back on the rails.