Hi Whammo,
Usually at the beginning, the game is all about exploring nearby solar systems for a suitable colony location where you can expand to using your colony fleet.
You can explore systems by sending any one of your fleet but it is highly recommended to use a combat fleet so if they get ambushed by pirates they can defend them self.
In addition you can research new technologies from the colonial or economics research trees that aids your new colonies in growing to their full potential.
When it comes to mining with your mining fleet you can keep them in your starting system it is full of minerals at the beginning of the game so you do not need to worry about it for awhile.
You can find more info about these actions outlined in the tip menu that can help you figure out how to do things, however in regards to what to do is up to you and your play style.
I am sorry at this stage of the game you will not find any tutorial in the game, my focus was on providing information on how things work not so much how to play it, but i will look into providing some outline on how to start the game in a future update.
If you stuck at something please let me know and i will try to help you out!