If we're talking free roam:
Starting from your apartment (if you have one), figure out a clean and efficient path that hits up each convenience store ($~1800 average) with regular stops at gang attacks ($~2000-2500 average, but make sure you comb the area well and look for every enemy you killed). Pick up the nicest looking car along the way to sell to LSC. Every time a crate drops check the map to see where it is - if its close enough and no other players seem to be headed for it or close to it - go for it, If not its super far, I'd avoid it if you just want quick cash, no need for confrontation otherwise. Simeon's vehicles are always going to pop up and usually net a decent amount, worth going after if they're nearby enough and no one else is bothering. Armored trucks are always a good way to go - my personal method is stopping my car in front and taking out the driver and passenger then quickly pulling around back and bombing the doors (from my car, its quicker/easier) then quickly getting out to collect. By the time you've run around enough you should be able to pick up another nice car to sell to LSC. Rinse and repeat all this and you can actually make some pretty damn good cash in free roam, not to mention rank up quite a bit too depending on your level. Add in good bounty collections if there are some and that just adds to it.
GANG ATTACK MAP (colored number are what time they show up, numbers are what level they unlock)
If making money is all you want to do at the moment and you can't shake the cops, don't hesitate to call Lester to get rid of them so you can get back on track - sometimes $500 is nothing compared to the time you spend on the run.
Here's some important stuff to remember when trying to save up cash:
1. Try to avoid unnecessary confrontation. You're not going to make a lot of money if you spend it all on health insurance from dying and ammo, not to mention all the time you waste that could be spent making money
2. If it looks like someone is following you, try to shake them before continuing your money-making mission
3. Be conservative with your ammo and go for headshots. Try to avoid using explosives
4. Try using your personal vehicle at all times so you can keep on-track
Outside of free roam, races, parachute jumps, survival, and some missions (the shorter ones, because of their time/money ratio) are all rather rewarding for what you put in.
Anyone who says making money is impossible in this game is either lazy, stupid, greedy, impatient or simply doesn't understand how progressive game-play works. Or some kind of mix of the above. I personally find it infinitely more entertaining and rewarding to actually earn money.