Play a hyper carry and get extremely good at them. Morde, Olaf, Jax, and Tristana are all hypercarries but not only them. Focus on being able to 1v3 at least.
Best of luck!
problem with most of the advice in this thread is that they advice is from ppl who've never been at 500 elo. 500 elo is a different beast to 900 elo, it's different to 1200 elo, it's different to normal games.
you can't expect to use the same strategies at different elos and expect to win consistently. at 500 elo, these are so many more weaknesses in the players that you can ABUSE the **** out of them. not over extending, playing safe, all that jazz.. simply isn't the best way to go about winning at 500 elo. of course you don't want to give free kills, so warding is still a good idea - but say you don't have an area warded - at 500 elo, it's generally a good idea to chase a low hp enemy into that area to secure a kill. the point i'm making is that at 500 elo, you have to make SMART, AGGRESSIVE plays that get you FED. that allows you to CARRY.
another important point to make about 500 elo is that the players there don't PUSH enough - they hardly push at all.. in fact they only push towers when allied minions are conveiniently knocking on the enemy turret and they happen to be in the area.. this leads to extremely drawn out games that reach 40mins +, everyone gets their end game build, and it takes not 1, maybe 2, but often more than 2 5v5 team fights at the 40 min mark and win fight or lose fight, ppl just heal up and come back for the next round of fighting - NO ONE PUSHES
you can abuse this by playing a champion who can push - this means that ap casters are a bad choice if you want to hard carry at this elo.
personally i played jungle udyr to carry myself through this elo range, and jungle udyr is perfect for pubstomping because he's an insane duelist when fed - has crazy mobility and pushing power, has enough cc to gank (it's not hard to gank 500 elo players, u just walk up to them and hit them a few times and they die before they realise what's going on), can survive fights and push towers after fights. you don't usually have to worry about full on team fights.. the enemy is usually so uncoordinated that you can 1v1 each of them even if ur team is derping somewhere else. a fed udyr will decimate anyone with no amr easy as pie. and NO, ur primary goal isn't to duel ppl and kill them, even tho you're very capable of doing that - ur primary goal is to push towers.. so if u find that a lane is undefended, which often there will be, just push minions up to tower and maul that tower to bits - often enemies will leave you alone to push a lane for more than a minute before they react and send someone to defend.
i like to push bot or top, and ward the adjacent enemy buff, so that when i see them coming, i turn and kill them and go back to pushing the turret.
at 500 elo, it's mostly a 1 man show. if you don't push towers and keep the show going, it's gonna drag out to late game when everyone has late game build, and it's just coin flip to see who wins the team fight. sure you have a slight edge in that you know who to focus - but ur team mates do not, so ur contribution to the team becomes diluted. winning a fight becomes a crapshoot - and you never know if that fight is the FINAL fight, because ur team don't necessarily push for win after winning that 'final' fight - often the go back to heal - you have to sit through round 2.. maybe you lose round 2, but for the love of god, the enemies give you a chance for round 3. it's a terrible elo to play at if you don't snowball off the early game and just push to a win in the mid game.
lastly, when you get out of 500 elo, doing the same things that allowed you to be successful at 500 elo, will get you destroyed at 700 elo. trying to 1v5 the enemies will actually get you killed - surprise surprise. unless you want to get kicked back down to 500, you've got to change up the way you play.. find other weaknesses in the players to abuse the **** out of.
in conclusion - you have to carry yourself out of 500 elo, u can't sit back and play support because all that will happen is that ur carries will derp around for 40 minutes.. and coin flip a few fights to see who gets to take the nexus. don't expect to coin flip to a higher elo, even if you 'play better' than everyone else in the game. the key to getting higher elo, is that not only should you be able to win against your opponents, you should be able to win against your own team, if you had your opponents as your team mates.