Got to the Eranin Federal Distress location and join the Eranin forces. You will be fighting mostly federal fighters with weak shields and hulls. Even with one laser you will be killing them quite easily. Keep doing this until you have enough money for a second laser which will make the money come in quicker.
1. Do NOT join the Federation, you will be going PvP and will die in seconds unless you have a very well kitted out ship.
2. If you see a player controlled ship on the Federation side, assume he is in a ship far more capable than yours and get out ASAP.
3. Don't fly to a station when you are finished playing. Just Save and quit, this will mean you just keep appearing in the Eranin Fed Distress location.
4. If you are in the starter ship just fly til you die. It is pointless flying back to a station for repairs.
If you die in the starter ship having made less than ~2000cr, alt+tab and end the Elite Dangerous process. When you rejoin MP you will be back at the Eranin Federal Distress location.
Each kill nets you 500cr and in one 2 hour session you could easily make enough for an eagle or to upgrade your Sidewinder. Or do this a few times if you want a hauler to go the trading route.