Place the Training Dummy by right clicking. Pick it up the same way, if you are not holding a weapon from this mod, sword or bow.
You can hit the dummy infinitely, it will never break from projectile or melee damage; however it does when set on fire, exploded, or when it falls from too high. A glitch has been reported on SMP where a training dummy will fall through the block it is placed on. This can be fixed by placing a torch on the ground, and placing the dummy on that instead.