DeLorean engine mounts P/N K100778 are thick rubber pads with metal adapters that cradle the crankcase between the arms of the rear cross member. They can be checked by prying up on the engine near the mount as shown in the video below. If the mount separates in two, or there is visible dry rot, it's time to change it.
To replace the mounts, remove two 10mm (17mm socket) nuts (Item 5 in the illustration) on either side of the mount (one behind the frame, one forward of the frame). In most cases you can then tap the stud out of the engine cradle and replace it with the new one in the kit. Use a brass or plastic tool to drive out the stud (see caution below) as you don't want to damage the threads until you know the stud will come out. You will notice that there is a bent thread on either end of the new stud to ensure that both nuts tighten evenly.
CAUTION: In extreme cases, the mounting stud may be stuck in the lower mounting boss on the block. If this happens, DO NOT attempt to drive the stud out of the block as this typically indicates a severe corrosion issue and you can damage the block. You'll have to clean up the threads on the stud and leave it in place, using the new nuts provided.
To remove the mount itself you will need to lift the engine slightly (use a floor jack and appropriate padding) and access two 8mm (13mm head) bolts (Item 7 in the illustration) that are holding each mount to the frame. One of the right hand bolts also secures the engine ground braid wire. It is extremely important that the ground be clean, and we recommend replacing at least the bolt holding the ground wire to the mount.
Updated 6/8/2016 DAS [Edits, links]