Select the 'Medals' icon on the left of your home planet to be able to read a description of ALL the awards currently available. When you start any mission you can hover over the greyed out Medal to find out it's general category and if you need more information you can refer to it at the Medals screen from your home planet. Listed below are some of the Medals and their requirements.
Lazy Medal Win the mission without moving any unit.
Grenades Only Medal Win the mission using only Grenades as weapons.
Flawless Medal Win the mission without any of your units taking any damage.
Solo Medal Win the mission using just your own unit (this may require removing friends)
Boot Camp Medal Win the mission with a team of three level 1 friends (can only be completed when you have reached level 15 or higher).
Win 5/10/20 Times Medal(s) Win that meteor the specified number of times.
When you select 'Weapons' from your home planet you will find that you start with a bazooka and a grenade (both at level 1). To upgrade or learn new weapons you need a certain number of crystals and metals. Listed below is the combination and numbers required for the next upgrade of each weapon. When you have the required amount of crystals and metals to upgrade your weapon of choice, select 'Research'. The 'Research' process can take time to do but can be shortened if you have friends with the application to help you. If you don't want to wait for the 'Research' to complete you can always click 'upgrade now', but this will cost Playfish Cash.
These are earned by visiting your friends’ planets. To find your friends’ planets select 'Galaxy' while on your home planet from the icons on the left. When metals are availalbe the metal dispenser will glow. You can only collect metals from each friend once per GMT day so when you have collected metals from a friend you need to wait until after the next midnight GMT before you can collect from then again. Below is an image of what the metal dispenser looks like when it is not glowing.
These are earned by completing missions successfully. When you destroy robots they will drop the crystals which are then automatically collected. If you fail the mission you will not receive the crystals.