Provided you've done the "Welcome mission" and got your 10k Credits, go to outfitting and buy D-rated modules. They are lighter and allow your ship to jump longer distances. Aside from that, buy the best Frame Shift Drive you can afford (Maybe it's D, maybe C. Sell you guns. That will make traveling around much easier. Move a couple of jumps from your starting system (especially if you're playing in Open)
Pick a station that you like, and look for courier data missions. The fact that you're transporting data instead of cargo means that you won't lose jump range, which, in a base Sidewinder, isn't really good.
Be sure to always return to "your" system for next batch of missions. It's important, because as you gain reputation with local factions, the mission rewards skyrocket to surprising heights.
Another thing you could do (If you didn't sell your guns) is to find a Resource Extraction Site (Any except Hazardous), fly around a find a bunch of cops killing pirate ships. Keep close and "steal" their kills by shooting the pirate just before they die.
Though this activity, although quite safe, brings a couple of dangers, like getting wanted if you shoot an innocent ship or a cop instead, or getting dead in general if you aggro pirates on you.