Right now you want to do Robigo Mining smuggling runs (look up Robigo on the Galaxy map). The best ship for this is an Asp Explorer with about 32 tonnes of cargo and a lot of fuel.

The key points are:

• Take no more than five missions, but make sure you can take five given the cargo amounts. The more missions, the more people are going to try to kill you. That's bad.
• You should try to get at least $4 million per mission but when you start you may only be able to get $2-2.5 million per mission.
• Avoid surface missions if you can, they take too long. If you're not getting non-surface missions go ahead and take them.
• To get new missions log out and go to a different game mode: Solo -> Open Play. Open Play -> Private game. Private Game -> Solo Play. Rinse, repeat.
• Fire once on system authority ships when they interdict you to stop scans.
• Kill interdictors if they're weaker than you or they'll just keep coming after you.
• You need to be able to go about 420 light years without refueling. Don't waste time fuel scooping, and become vulnerable, just carry more fuel.
• Approach stations from the side of the planet to be lined up with the station entrace. Don't worry about outposts though. The landing pad always seems to be as far away as possible regardless of which side you come in on.
• Run, run, run. Haul ass into and out of stations or you will get scanned.

I've run this with a stripped down Asp Explorer for maximum jump range but now prefer having weapons to kill the annoying little Haulers and Vipers that come after you.

Also you need a 5A shield, not a 3A shield like so many people say. The 3A lasts about half a second while the 5A will last long enough for you to get away when interdicted. You really need a 5A if you're going to fight.

My current loadout with 32T, weapons, but only 23.34 LY jump range ($28.5 million):
http://coriolis.io/outfit/asp/05A5A5A4D4A5D5C1b1b1818181800040404f64a0202020101.Iw18WQ==.Aw18WQ==

Stripped down loadout with no weapons-- 25.66 LY jump range ($17.3 million):
http://coriolis.io/outfit/asp/05D5D5A4D4D5D5C----------f64a0202020101.Iw18WQ==.Aw18WQ==

Max jump range but only 24T and no weapons-- 27.49 LY jump range ($17.1 million):
http://coriolis.io/outfit/asp/05D5D5A4D4D5D5C----------f54af302020101.Iw18WQ==.Aw18WQ==

Also do not ever sell your Asp Explorer! It's the most useful ship in the game and you will constantly, constantly come back to it.