Map control is important, but also how you place your units on the map. Look for cover, use buildings to your advantage, and take note of choke points.
Stick to a structured build order with a few variations so you can react and counter the units your enemy is fielding. Look for build orders on YouTube.
Plan ahead on how you’re going to spend your resources. The best build order means little if you’re floating resources – timing is very important in CoH. Know the costs of everything you’re building/training.
Unit preservation is vital. Retreat squads before they get wiped and repair damaged vehicles. Veteran units are much better at combat. Use special abilities like smoke, artillery strikes, grenades, and mines to fight effectively.
A lot of the game is about the feel of any given match, and that will take time and experience. Sometimes being aggressive with your vehicles can pay off, other times it pays to play defensively.