Hexagor is all about raging with with nothing but hexes. You start with a base, and from there, you click adjacent hexes to expand your territory. The more hexes that are under your control, the more towers you can build, and the easier it will be to lay waste to all those who oppose you. Or team up with another player to make your enemies cower. But be sure to keep an eye on your own base when you're busy waging war. The best defense might be a good offense, but you still have to defend.
Move the map around with WASD, or by clicking and dragging. But you'll be spending most of your time madly clicking hexes in an effort to expand. The time it takes to capture a hex varies. If you only have one adjoining hex, it can take some time, especially for mountainous terrain, but if you have another hex all but surrounded, you can scoop it up in the blink of an eye.
If one of your hexes is under attack by an enemy player, click it to defend and to place it on lockdown for a few seconds, preventing any further attacks.
Towers can be used to stage a conquest, which is a way in which to capture 4 tiles quickly in a straight line, assuming there is no town or mountain in the way.
Conquests are a great way to quickly make an incursion into enemy territory, and to avoid obnoxious defenses.
If you're looking to capture a mountain hex, surround it first. It'll ultimately save you time.