In Empires and Allies, missions and friends are the back bone of this war themed game. Missions are what net you the most experience and progresses the storyline while friends give out perks for interacting with them.
As long as you keep progressing through the campaign and gaining new allies, you will surf through the levels quickly and without having to spend any real world cash.
Combat Missions
Mission are where the plot of the game progresses. Usually you get an agent from the Dark Alliance, ready to derail your hopes for revenge. Missions gain you the most rewards through loot and experience drops. They also net a good amount of gold, liberty bonds and other items the first time though (subsequent play-throughs of cleared maps do not drop any bonds or schematics).
Invasions and Invading
Unless you used an embassy, enemy computer controlled and human players can invade your island. An enemy basically can attack an unprotected part of your land. To prevent this, place land troops around your island. Make sure the places you put your units down isn't land you need later as once there are out, they stay out.
Invasions are to be taken down swiftly as the longer an enemy stays on your land, the longer they can steal resources from you (unlike allies which share). On the flip-side, you can invade allies and occupy their land. You can gain loot and start gain reputation as an invader. Keep in mind that other players including the one you are invading can attack right back!
Helping Friends
Like all Zynga games, this game requires a lot of help by friends. You can visit linked friend's islands and speed up their crops, farm their farms, trim their trees, and even loot the rent from their houses.
You can also request friends to staff open offices (most government building require staff to become complete; in turn netting you more population) and send useful items back and forth. Being a helpful friend can help you expand your empire faster.