OK, PUGing can be a pain. There are several things you can do to help yourself get into a PUG Group, although it depends on server to server. So the following details are for my server:
Download yourself the GearScore Addon, everyone is interested in it nowadays. It's a right pain, but you just have to live with it. Secondly, achievements, achievements are important and most people now won't give you a chance unless you have the achievement. If your struggling to get this achievement, because you can't go, (it's a vicious cycle, I have been in it) then there are several things you can do to try and get around it.
- Get a friend that has the achievement to get you in.
- Have a high gear score (this can be done without raiding, just doing HC's)
- Try and "blag" your way in.
In regards to getting a good group. Mostly it's down to luck, but you can check your group to see roughly if you will do well or not. To check your group do the following:
- Check other people's gear. if it's good chances are they are going to be OK, unless they have been boosted. The way to tell if they've been boosted is to see how many good items they have, if they have a lot but by talking to them, not a lot of experience, chances are they've been boosted.
- Check people's guilds. Learn the good guild's on your server, and when you join a group, check to see if the guys are from these guilds.
- Ask them questions. Learn yourself the IN's and OUT's of ICC, and when you join a group, ask them some questions about it, like what do they think work's best on this boss, that tactic or this tactic. This will give you an indication of what they are like.
This is going to be very hard if you haven't been to ICC once, as no one will let you in because as you've said yourself they want a good group and to do it quickly, not someone they have to teach. If you can, go with a friend who has previous experience. If not, when you get into a raid group, try and befriend some people and impress, and just say, "Hey, next time you get a group, whisper me and ill join :)"
This should help you get in.