Moving and shooting, obviously, are the first step to playing Starblast. You gotta master it before you get into the action. You have to hold right click to move around. Once you get used to this, you can start to use RCS(See post about RCS in Winning Tools). Pretty simple, eh? Now to shoot you press the left click button. If you want, hold the left click button and you will be shooting constantly. Cool. Now move and shoot at the same time. This is how you mine and battle. When you become comfortable with moving and shooting, start to level up your ship.
By mining asteroids, you also have to gather the gems. Gems are essentially the only way to do anything. When you get enough gems, you can upgrade your ship's stats(See post on Upgrades in Winning Tools), or you can level up a tier and get a more suitable ship for surviving. This will begin to help you in the future.