By request...
KingLeerUK's Hawkmoth Piloting BasicsNo warranties are expressed or implied. 
"W" - upthrust
"S" - downthrust (but not very much)
"A" - rotate left
"D" - rotate right
Mouse Forward/Back - pitch nose forward/back
Mouse Left/Right - roll left/right
"SHIFT" - this is a thrust modifier, it changes the vector of the UP thrust to FORWARD thrust when held, when released resets to UP thrust
All of the rest of the controls are the same as other vehicles.
The trick with VTOLs is finding a balance between upward thrust and forward momentum when trying to target something. Your friend in this adventure is changing the throttle behaviour to work with your preferred piloting type using "K". I prefer to keep my throttle unlocked, (the default), meaning that I have to hold "W" to maintain up or forward thrust (depending on SHIFT modifier). I prefer this for most flight modes, but using "K" to set a hold/ramping throttle and ramping to about 5/8 throttle lets me establish a relative "hover" state that is good for LtGauss sniping or LRM platforming.
The big trick with the Hawkmoth is keeping it alive. The thing has tin foil armour and a shot into your side will pretty much wreck the engine in one salvo. If you are engaging air-to-air be sure to try and face a target and not let an enemy get a good hit on your sides. On the plus side, if your engine is taken out, you can power down and ride-your-wreck down to a safe altitude to bail out, assuming that AA isn't ripping you a new one.
Keep an eye on your armour, as with several of the other vehicles in the game, we don't have full audible feedback *yet* for taking damage depending on the surface type and the incoming weapon.