As others have said, do the training missions to learn how to fly and dock, use the galaxy map to jump between stars, and so on. As for general hints on what to do:
You have a basic discovery scanner in your ship. In your right hand panel, go to the fire groups tab, and assign a fire button for the scanner. Now, when you look for stars for which you have no system data (the "show system map" icon is red in the galaxy map), jump to these star systems. On arrival, stop and face the star. After a moment, you should see the "discovered a new celestial body" message, and can target the sun. Do so, and your ship will begin scanning the star. While it is doing that, use your discovery scanner (hold the button until its finished). You may discover more system bodies (planets etc). When the scan is finished, target these via your left hand panel (navigation) and fly towards each, until it begins scanning them. When you're near that object, use your discovery scanner again (it has a limited range, and may pick up more objects now). Once you have scanned a system, you can fly to another system at least 20 ly away and sell your scanned data after landing at a station: Use to the Universal Cartographics function in the station menu.
As others suggested above, use the bulletin board in stations to find missions. I'd suggest you take only transport missions at first. Smuggling may pay more, but you must know what you're doing else you may end up dead or with huge fines to pay. You should avoid combat missions until you have mastered the training combat missions and know the basics of flight and combat.
You can also trade. But know that your starting Sidewinder has very little cargo space, and you only have very little starting cash, so it will be slow. Check the system map to find out what type of station you're at (for example, industrial, agricultural, refinery etc) and what other stations are in the system, or in systems nearby. Then check the commodities market and see what items are in stock. For example, if you are at an agricultural station, you will find things like animal meat, grain, and such. In the detail view for each item you will see what type of stations will buy that commodity (take that as a rough guide tho...its not 100% reliable). Buy as much as you can of these, and fly to a station which wants that commodity. Sell (with hopefully a nice profit). Repeat
Once you have earned a little cash, you can either upgrade the components of your ship (in outfitting) or buy a bigger ship. Its up to you
Hope this helps a bit. The galaxy is huge, and there's a lot to learn to be successful. Stay at it, it can be very rewarding!