When you go to an area on the main map to travel to the DLC areas it will tell you what level you 'should' be to complete the DLC. I've only done Dead Money so far, I think it told me I had to be 20+ (I was about 28 when entering).
My advice is also wait until you are near the end of the game as some of the DLC alludes to characters you might not have run into during your game if you go in too early.
Both correct, good advice. No, don't complete the game first otherwise it'll end your save if I'm not mistaken. Fallout 3 had the Broken Steel DLC to extend the game, I don't think Fallout NV has anything like that. One tip, Lonesome Road can be fearsome. A lot of powerful enemies there. I've not done the Sierra Madre one, but all the others have been reasonably easy. Old World Blues has a lot of fighting but isn't difficult, the same can be said for honest hearts.
I've almost got all the achievements off this now, just need the Sierra Madre ones and the Gun Runner's Arsenal Challenges. Need to eat 10,000 points of food too, which is taking ages but I'm at 8,000, shouldn't take too long. Still got the entire main story to do as well, so the oppurtunities there. The GRA one's seem unecessarily difficult or bothersome, as well as expensive. I think I'll create a parallel save with my character so that I can do the challenges without it impacting upon my preferred story choices.