What are some tricks that are really good to know for new players?
I recently found out the trick where you can spawn the dropship on you if you drill down and then have your engineer block the hole.
What are some other similar tricks which can be really helpful
Lootbugs eat dropped loose minerals, and when killed will yield a larger amount than what they ate. It can be worthwhile to let lootbugs munch on some stuff if you plan to return later, to harvest a bigger bounty.
Drillers: Once you unlock the Experimental Plasma Charger (EPC), this can be used to mine resources. You charge a full shot, fire, and fire a small shot to burst it. Getting the timing takes a bit, but it's very useful. Especially for ceiling mining.
Scouts: Light. The. Rooms. That's your main function, and it's so helpful. Also, fetch minerals. You can do a grappling hook (letting go before you hit the destination) to momentum fling yourself and then finish with a power attack to make a landing area in a wall to mine from. This is a big time saver.
Opinion - scouts should call the MULE sparingly. They can get to the MULE way faster than it can get to the, and you're also delaying all the other, slower moving players from using it.
Gunners: Barrier is so good. Save it for when you really need it (especially for picking up others. Ziplines are like crappy grappling hooks that everyone can use. Making them cross over each other in x patterns can be helpful so you're able to go faster (on a downward slope) both directions.
Engineers: I may not be the best person to ask. I find Engineers very tedious and boring. Too much gun hammering and refilling of gun ammo, and no particularly useful mobility tools (the platform gun is the meh-est of the mobility tools, in my opinion). Other may have differing opinions on the matter though.
Welcome to DRG! Rock and Stone, Brother (or sister or sibling)!
Have your turret(s) at least partially covering a wall or other vertical surface; generally dwarves have an easier time taking out lots of bugs on the ground, but struggle a bit with walls and ceilings.
Related to the above, consider having your turrets facing backward toward you, at some distance. They'll cover your back and alert you to incoming enemies you can't see.
Go ahead and platform every vein of ore or mineral deposit you can see when you enter a new area. Your Scout will appreciate it greatly.