Artillery use is fairly straightforward. You go to the war zone maps. Place artillery next to your target. When you attack that target the artillery tab will show up on the right side of your screen. Click the tab, click the artillery, click the location you want the artillery to attack.
Level 1 artillery will give you 3 salvos. Level 2 artillery will give you 5 salvos. Level 2 artillery can be placed a hex away from the target. Clever use of level two artillery and airfields along with alliance coordination can make strongholds significantly easiest to complete.
Airfields are a bit harder to understand. These fobs are not the same as the airfield in your base. To use an airfield go to the war zone map. Place an airfield and park your base next to it. Your base can now attack or scout any hex within two hexes of the airfield. This is an important but subtle distinction. The airfield does not extend your bases scouting range the airfields scouting range is 2 hexes and by touching it you are allowed to use the range of the airfield. Just as an example you might use an airfield to attack a helicopter forward operating base that is supporting a bunker by attacking over the bunker with the airfield.