From left to right, Icy rock, Cobaltite rock, and Iron ore. All sitting atop light rock.
So, you've landed yourself on an asteroid somewhere. Tough. Well, no time like the present to play out your dreams of becoming a spaceman! But first, you need a spaceship.
First order of business, open up your inventory with C. Drag your Cobalt Pistol, your Iron Drill, and a Mineral Extractor, Ore Smelter, and Crafting Table to your placement bar at the bottom of your screen.
Now that that's all sorted, take a look around you. Nothing but space in all directions except down. Move your mousewheel to select your Iron Drill (Or use your number keys), click and hold to start mining the delicious minerals from the floating rock.
What you're looking for at the moment is brown dirt that has cracks in it (Cobalt), lighter brown dirt with black flecks in it (Iron Ore), and tannish rock (Icy Rock).
You're probably going to run into some other things out there aside from yourself, so keep your Pistol ready. This doesn't use ammo, so you can blast away all you want. If you get too near the green blobs they will launch purple missle-like objects that will track and attempt to hit you, they don't explode however they will damage you repeatedly, taking them out from far away is easily done. The ones you have to watch are the purple guys, with their teeth. Floating back and around as you pew pew will keep you relatively safe. Just don't fall too far off the asteroid.
Now that you've gotten all the minerals you can stand, find a nice spot to plop down your first three manufacturing blocks. So you don't lose where you are, hit B to create a Beacon, and give it a name. Place it by clicking, and you'll see an orange target reticule to guide you back if you get lost.
When you're ready to extract minerals and craft, open your inventory back up with C, and drag your minerals from your placement bar back to your larger inventory before interacting with your workstations.
To make all the blocks and items you'll need, see: Recipe List
Once you do that, it's time to blast off! To get started, take a look at: Shipbuilding 101