If you are laning, the most effective way for getting more gold by far is last-hitting. There are many other methods out there, but they're most likely not the ones you want to hear.
You may hear of last-hitting a lot. Basically, last-hitting consists of waiting around until the minion has a health low enough until you can kill them with one hit. This increases your chances of getting the money from a minion kill, or "creep steal" by maybe 40-70%.
Good last-hitters can get 100-200 CS in 20 minutes. That's a lot of gold! Combining that with the gold you gain periodically and whether you're slaying a siege minion,
You can probably afford an Infinity Edge 20 minutes into the game and then some. This is considering you haven't killed a single champion yet.
With this, you can branch out on either being a team player or just keeping to farm, as the difference to you personally will be considerably more miniscule. Decide for yourself, but you'll be kicking ass either way.
Learning to last-hit takes time, but if you do it right you can become an extremely formidable force. Every good player should know it.
Best of luck. This will be helpful:
EDIT: The record was set by CLG.EU (my personally favorite team) in the Season 2 LoL World Championships of 300 CS in 23 minutes. That
would be approximately 6400 gold.... from farming.