Learn Russian: Обычно пилот летает очень быстро.

The adverb обычно (usually) tells us this is a repeated, habitual action rather than a single trip in one specific direction. For habitual round trips, routines, or general flying abilities, we use the multidirectional verb летать. If the pilot were flying to a specific destination right now, we would use летит.

I always mix up the forms of the two 'to fly' verbs. How does летать conjugate compared to лететь?

Летать (the multidirectional verb used here) is a standard Type 1 verb: я летаю, ты летаешь, он летает, они летают. In contrast, the unidirectional verb лететь is a Type 2 verb and has a consonant mutation in the 'I' form: я лечу, ты летишь, он летит, они летят.

Does летает mean the pilot is flying as a passenger, or operating the plane?

It can mean either depending on context! In Russian, you use летать (or лететь) whether you are the pilot flying the aircraft, a passenger sitting in the cabin, or a bird in the sky. If you needed to be highly specific about operating the controls, you would say управлять самолётом (to control the plane).

Could очень быстро go before the verb летает?