I've blogged about general tips for PuGging before, but I just thought I'd go into more detail on exactly how to get into good quality PuGs.
1. Always make sure to be in LookingForGroup chat (and Trade chat if possible).
This means joining as soon as possible when you log on. One line of missed Trade chat - "LF1 ranged DPS for Ony10" - could mean a missed opportunity. If you're on a bank alt or you don't want to be in any specific raid in the LFG tool, join via a level-appropriate zone (eg. Elwynn Forest for low levels or Storm Peaks for 80s) so you can at least watch the chat.
2. When in LFG for a specific raid, have a personal note.
There will be 3 others of your class sitting in LFG if it's a popular raid (particularly if you're a hunter like me!); you need to stand out. Having a note that says you're well geared, do 6k DPS or have the Achievement for the raid you're after can help distinguish you from others.
3. Sell yourself.
Most PuGs will ask you to whisper your Achievements to gauge whether you're competent. If you don't have the Achievement, link what you DO have - 4/5 or even 3/5 for Trial of the Crusader can be enough to get an invite, since it at least shows you can get past Faction Champions. Alternatively, offer your experience - "I have a main that has cleared this place", "I haven't done Ony yet, but I've killed Algalon".
If you don't have any experience, you'll have to wait for PuGs that don't ask for Achievements (some will just ask for stats and spec), or you can try and persuade them to take you by saying you've read the strat and watched a vid of the fight. If you come across as confident that you won't stuff up and aren't just a 6 year old kid, sometimes they will take you.
In any case, if you haven't already got the Achievement for killing the boss, remember that they are taking a risk with you - if you say you do 6k DPS even if your stats are low, make sure you do 6k DPS, otherwise you'll get a bad reputation. Don't make the same mistake twice - your guild may tolerate you dying to Ony's Deep Breath every fight, but if you stand out to a PuG as a noob, you're not doing yourself any favours for next time.
4. Know your guilds and fellow PuGgers.
If you PuG frequently, you'll start to recognize some of the other PuGgers. Try to remember which are good and which bad so that you can avoid getting locked to a raid that may not get completed. Similarly, if the people are from a reputable guild (good raiding progress, no history of ninja-ing), you can take a chance on them even if they look undergeared or Achievement-less.
5. Pick your groups.
If you're hoping for Keepers onward in Ulduar, don't immediately join a fresh run unless you have plenty of time or you know it's a good group. Sometimes it's better to wait for a chance at a half-cleared run, as you don't have to spend time on the first few bosses.
Make sure at least one person in the group (preferably the raid leader, but not necessarily) takes charge and knows what they're doing, like organizing tank/healer assignments or outlining the strat for the raid.
6. Inspect people.
I generally do this with every other hunter in the raid, if only to gauge my chances of getting loot. Inspecting the raid leader can also be useful; if they're severely undergeared and under-Achieved they may be looking to get carried through fights and not actually know what they're doing. If I can see a certain problem that keeps cropping up with one person (eg. a tank or healer), I'll inspect them as well. Knowing where your fellow raiders are at can help you decide to stay or go.
7. Know when to stay or quit.
If you're in a terrible PuG, it will usually fall apart by itself. However, if it doesn't and you can see that that the reason you're wiping is because of some key event - not enough DPS on adds to get them down in time, tank always dies at the same point in the fight, the same 3 people always die at a certain point in the fight and leaves the raid short-handed - leave the raid and be polite about it.
If you're in a raid where it's slow going but you can see an improvement with each wipe, think about sticking it out. I've been in PuGs that wipe several times on bosses, but manage to pull through in the end after getting more experience. Sometimes you can even help - point out where things are going wrong and suggest a solution, but again, remember to be polite.
8. Take a chance.
You'll get your share of terrible PuGs, but you'll also get your share of really good ones. Be willing to risk your week's raid ID for a chance at getting something beneficial out of it; if you get one piece of loot, one more boss to add to your Achievements-in-progress or even just experience with the fight, you have one more thing you can use to try and get into a better PuG next week.