I just recently bought a 2011 Giant XTC. Today was my first ride on it and I had the chain come off the crank twice once a two different down hills and it seemed like there was some jumping around on the cassette. I'm not really too sure what it could be. Could it all be fixed with some rear derailleur adjusting?

Adjusting the RD trim, will help some of the skipping around in the rear, but not correct the chain dropping in the front.

It sounds like your dealer did a fairly poor job setting this bike up. You could look up various tutorials on the net for adjusting front and rear derailleurs. Or you could go back and ask the shop do the job right.

BTW- if the drive train adjustments are indicative of their overall work quality, I'd speak to the manager and ask that the entire bike be checked over.

what is the TD trim is that on the rear derailleur? what could i do about the chain dropping in the front?

A typo, I've since corrected. It's RD trim and yes it's related to the rear derailleur. As I said you have two separate issues, one in front and one in the rear. By trim I mean the centering of the chain on each sprocket. It's adjusted by the threaded barrel that adjusts cable length. But there are other adjustments, some of which are critical to prevent something like the derailleur from going into the spokes.

The front derailleur also needs adjusting to prevent the chain from dropping. There are too many possibilities to go into here which is why I sent you to tutorials.

Overall the bike seems to be very poorly assembled, and just solving the obvious problems won't address the unknown ones. Even if I had the time to walk you through quick fixes, it would be a disservice.

You have 2 choices, either bring it back and have it thoroughly checked over the way it shoild have been before they gave it to you. Or look up various tutorials for derailleur setup and adjustment and study a few until you have a sense of what's involved, then do a complete setup and adjustment process from the beginning, checking and correcting, if needed, every detail of the assembly and adjustment.

Alright i looked up tutorials and i think i got my problem fixed. went on a second ride today the bike worked very well no derailments or ghost shifting. Thanks for the diagnosis.

You're welcome, but I didn't do anything but encourage you do do the job right.