First of all in single-player missions you don't need to control the whole map just focus on the objective.
In multiplayer mode the first team to take a neutral oil derrick gets a 100 coin bonus to be spent that turn.
Check enemy firing ranges by holding down on them and move your units appropriately. You can always use the undo button when positioning your army if not satisfied.
Take advantage of that minimum firing range. If the enemy has Snipers eliminate them by shooting them at point-blank range with Grunts. Same can be said for the Recon Tank against enemy Artillery and MLRS units.
If the enemy starts cranking out loads of units before you do counter them with units that deal splash damage like the Grenadier and MLRS.
Big units like the Cruiser and Bomber can do huge damage but if you leave them unsupported they'll be lously spent $. Deploy them when you already have cheaper units available to escort them.