Trading is only relevant in terms of civilian shipping, which will automatically establish itself as you build colonies, and wil provide you with a modest amount of additional income.
I don't understand how money works in this game, is it in the wealth tab? And what is it used for, stuff doesn't seem to have a cost, just a required amount of minerals.
Also, what should I assign commanders and such to? And what is a team in the academy tab? Sorry, far too many questions here
AFAIK wealth is just an abstract measure of your treasury; it probably has some uses, but the only one I know of is subsidizing civilian shipping.
Form teams first in the academy tab, they fill useful roles. Geo teams can increase mineral amount or accessability on a planet, but should be trained up on moons and low quality planets first, as they can exhaust their search, and you want to get as much out of your good worlds as you can.
Xeno teams are used to identify alien ruins, which can then be recovered by Engineer Brigades.
Diplomacy teams can be used to negotiate with enemies.
Spy teams are used to, well, spy on other empires.
Make sure to assign commanders with 30% bonuses to their respective teams, as well as assigning commanders with good bonuses to ships and planets, to prevent them from being culled. You can assign naval commanders to ships, and to staff positions, civ admins as planet governors, GF commanders as COs of ground units. When assigned, their respective bonuses come into play, which can be very helpful with something like a civilian admin with 30% pop growth bonus on a new colony, or 25% shipbuilding bonus on Earth.