Diplomatic relations with your neighbours are extremely important. Your nation can be destroyed if you did not properly set your diplomacy: you might make several enemies who could then form a treaty to fight you. This happens quite often.
Your nation starts out with 10 armies of 100 Cavemen in your capital; more can be drafted using the [a]rmy menu. Soldiers are used to occupy unowned land, to defend your own territory, and also to conduct war against enemy nations.
To occupy an unowned sector, you must have an army of at least 100 soldiers there, set on occupy mode. To occupy a sector owned by another nation, you have to declare WAR or JIHAD with them. Sectors can also be occupied by spirits with 100 units or more.