Currently, there are 3 different resources in Strike Tactics and 4 ways to gather them.
Carbon is harvested from flying worker units, the same units responsible for construction. Right click a tree while a worker is selected to begin harvesting carbon. The carbon will automatically accumulate in your inventory. Once the tree no longer has carbon, the worker will automatically move on to the next closest tree.
Ore is gathered by building a miner unit. Right click a patch of ore while the miner unit is selected and it will start to automatically gather ore. Unlike carbon, ore doesn't automatically go into your inventory - instead, the unit must drop ore into silos, which are small rectangular buildings. Build your silos in strategic locations. If you build a silo in a spot surrounded on 3 sides by trees, your workers might have a difficult time depositing ore.
Energy is generated by building power generators. These simply structures automatically generate a small amount of power over time. Be carefel about where you place power generators - when they die, their explosion has a blast radius and can set off a chain reaction to destroy other nearby generators. Because of this, you should build your generators far apart.
Aside from the methods mentioned above, you can also gather resources by building freighters.
Freighters are trade ships will travel back and fourth between friendly airstrips and generate any of the 3 resources, based on which option you have selected, each time they make a trip. The longer the ship has traveled, the more resources received. Keep your trade routes well-guarded and prosper.
Different units require different kinds of resources, so choose your worker composition (miners vs. carbon collectors) accordingly.
In Strike Tactics, there is a duality between air and ground. Unlike in traditional RTS games, where air units are generally there for support, the dynamic between air and ground is 50-50. Enforcing this dynamic is the fact that half of your workers are air units and the other half, ground - half of your resources are collected by means of air and the other half, ground.