I use lots of things. At garage sales, I look for purses & totes that I can cannibalize for handles & clasps. Often they are less than a dollar. I also use nylon strapping, sometimes covering with fabric from the bag. When shopping for premade handles, you need to consider the structure of the bag they are going on. Plastic handles can be very heavy and if the bag doesn't have enough body, they can actually pull the sides down. Big Box craft stores usually have a good selection, but do consider the weight. Leather handles are very luxurious!
As far as attaching them, the leather are the most straight forward. They will have holes pierced in the portion that go on the bag. You hand sew them with heavy buttonhole thread. Other purchased handles usually have metal round, D shape or rectangular rings. You make a long narrow rectangle of reinforced fabric and sew that to the bag. Some of the rings have screws so you can open them. In this case you attach the fabric loop, open the ring and insert then handle. If the rings don't open, it's a bit more tricky as you have to put the loop thru the ring and attach it to the bag with the handle attached. Use a zipper foot to get close to the ring. in either case, you can attach the loop to the outside of the bag or insert it in the top seam where the lining meets the outer fabric.
If you are interested, the best blog on purse and bag construction is Lisa Lim's U Handbag:
http://u-handbag.typepad.com/