Here's a little bit of what I do with heavybag lifts:
Make sure that the heavybags is (at least) your own weight. That way you are training yourself to lift someone else in your weightclass.
Remember, these are intended to work muscles essential for ground fighters (particularly for takedowns). It's my way of combat training for takedowns with something that builds explosiveness!
First: Do a straight lift. It's sort of a dead lift, pick the bag up against your chest, lean back and then lean forward and put the bag down. This should really work the core (mostly abs and obliques) as well as some in the legs.
Second: Do a shoulder lift. Pick the bag up, put it over your shoulder, do a full leg extension (I've actually seen guys stronger than I am do a jump from here to build the legs). Once you've completed the extension you can put the bag down or slam it down to complete the rep. (If you have a mat a slam is definitely the best way to go, if you don't then don't damage the floor)
Third: Do a should toss. (Only if you have a mat and open space to toss onto) Lift the bag and throw it over your shoulder. This is built to simulate a suplex style throw. It is really essential for building strength in the hips as well as the legs. (it's a great excersise for wrestlers, though suplexes are harder and harder to get in MMA)
Remember, with every lift you should lift the bag off of the mat in order to make sure that you are lifting it as far as you can to push your body as hard as you can.
Sig by Toxic
Barnett - Toquinho -Werdum - "Nurmie"
Z. Gurgel - Morango - Rocha - Tiequan