They can be pretty good instant fortifications to act as a fierbase. Using Aerodynes is pretty self-explanatory, but my main advice with Spheroids is to land in an open area so enemies cannot get close to you without getting shot at, and to point the bonudary between your left and right arcs as directly at the enemy as possible. This will allow you to hopefully use the firepower in both arcs, as well as both sides of armor. If your enemies can stay on one side of the ship and focus there, they cut the armor they have to eat through in half, as well as reducing your targeting options. It seems reasonable to assume that you'll have actual ground forces available, yes? If you can, use those forces to try and herd enemies towards the left/right dividing line, to make sure you can use both sides of your ship. Aerodyne vessels have more limited firing arcs, but can also taxi. You can simply turn in place to keep your nose pointed at the enemy, and pour fire into them. Remember that while some DropShips do indeed have heat problems, you can usually fire at least a couple arcs at a time, and those guns should be going full auto constantly.
Another thing to keep in mind is that the vast majority of DropShips are NOT massive combat behemoths, but fragile transports with purely defensive levels of arms and armor. A Union may be an enormous multi-kiloton machine of war, but that doesn't mean it can stand up to a heavy ground assault. The record sheets we got in the HexPack promotional PDF give it a BV ranging from just under 4,000 to a little over 5,000. This means it is theoretically about equal to a singe 'mech lance, likely of mediums and heavies, not assaults. This seems about right to me. If you have more than this coming at you, you'd best have ground forces or something to back you up, or be prepared to lift off NOW.
On the other hand, a dedicated assault ship like an Avenger or more modern vessels such as the Seleucus can very easily go through 'mechs like a giant lawn mower. >:D