I will usually just call them and maybe (Big maybe) see a small raise based on person raising.
You actually want the J to hit and not the A. If the J hits then you know you have the best kicker. Then if an A hits on turn or river you could have top two pairs and that is the best you can hope for.
I tend to throw it away with larger bets just because you could be facing big slick, AQ and get into kicker troubles when an A hits the board. The ugliest is when you face AA or JJ on a big raise and you call, half your outs are gone.
May call a larger bet if my AJ is suited and I have a chip lead on the table just for flush draws.
Are these cards suited or unsuited? I'll much more readily see the flop with suited cards, especially if it's already been raised. If I can see the flop cheaply I'll call with both. The flop will tell you everything you need to know.. If you flop a flush, you know how to play that; if you flop four to a flush, well, that's your call!
I find you are much better off to raise with this hand no matter what position, unless someone has already raised before you (may have to think about things then). I bet this hand as if it were AK.
Let me put it this way. I have done a lot more good by raising with this hand, than I ever have and will by simply flat-calling. You don't always get what you need, and you may lose a few times, but I am simply going by personal experience.
Treat it like a baby Ace (A2, A3, etc.). Players see a painted Ace and get excited, but 15 other starting hands are better than AJ. Given that your opponents are probably going to be hanging onto Aces, Kings, or Queens in some form or another, your chances of becoming a huge underdog on the flop are pretty good. I strongly disagree that AJ should be played like AK. I do agree that flat calling with AJ isn't a good idea, simply because I think flat calling is rarely a good idea with ANY hand. If it's not good enough to raise, it's not good enough to play. Get away from it.