Yeah, use the dungeon finder to get experience. If you're the weak link of the group, at least it's a random group with people from different realms.
If you fear that you're not gonna do well, you could of course just be honest and tell them you don't have much experience. I couldn't get in any raid groups to Icecrown Citadel before Cataclysm because my gear score wasn't quite high enough and I had no experience with the dungeon. So, instead of asking people if I could come along, I just started my own raid and told them I was an ICC newb. The raid members shared their experience, told me the important tactics and we had a blast.
Although people tend to be less friendly in pick-up-groups, the idea that only pimple-squeezing jerk-offs play wow is not true.