I take the role of buying wards upon myself. I quite often will get first blood so that extra cash I'll use on buying a ward or two. I often ask for whoever get fb to buy a ward to put in a key position.

In low ELO it probably isn't as important, because team members won't make the most of teh intelligence. But if you make a habit of buying them yourself, especially if you're successfully making kills or farming withough trouble, your team will play a little better, and hopefully see it as an example to follow.

The general rule is:
If you're doing well, plant wards near your lane, which should therefore protect you from ganks, and give you intel to complete ganks yourself.
If you do really well, be the good samaritan and do it for other lanes.
If you're solo queuing you'll notice benefits quicker, this should lead you to more wins... and then you'll eventually get to a point where other players will be doing it with you.

sight wards win games.

You should buy wards with any character you play. You go back to base, you buy your item, you buy whatever else you can afford, then you buy wards.

There isn't a use for that 180g sitting in your bank when you go back to base, especially if one kill from a ward will give you the cash back.

pretty much. As long as you're not getting absolutely dominated early, which should never really happen unless you're overly aggressive, you should get a ward or two at first trip back to fountain.
Only over aggeressive players should die multiple times during the early laning phase. In low ElO, players will be recklessly aggressive.
If you play burst/sustain damage characters, understand the limitations of your character.

Don't push too far if you have a champ that has no escape methods. Some champs are better than others at this. Understand how far you can chase and how much damage you can take before considering how far you're willing to chase. Most times, making them 'b' is as good as killing them. lvl curve, and unharassed farming is awesome.

Get in the habit of last hitting. not beating on whichever creep till its dead. Literally waiting till your creeps near kill them, and last hit. This way you'll never be pushed too far forward needlessly. Unless you and your lane mate can put some big damage on the turret, just wait. Mobs don't spawn any faster. Killing a wave in 5 secs or30 secs doesn't matter if noone is there. This way, you save mana, and you can leave more room for mid to help gank your lane.

Lol, my teams get into fights about this stuff every game: about who is buying the wards, carrying the elixir, whatever. At a mid-ELO, which is where I guess I am, most people only buy stuff if they're dealing with stealth heroes. Honestly, unless you role in premades, everyone is in it for themselves, so buy a few wards here and there at most unless you guys have a plan.

Trust yourself first and foremost.

A ward will save you from ganks, therefore you'll save money on deaths and score ganks.
It's dumb not to spend the money. The sooner you learn it, the better. It isn't necessarily up to any one player to buy them. But every player should buy them, for their own self preservation.

Mr 'stay behind theriver' rumble

I don't buy wards as shaco, I just use jitbs. This also works with Nidalee's bush traps, teemo's shrooms, heim's turrets (inadvisable), anything else that works as a mini ward.

For all other characters - go for it. But it rarely nets you kills, setting up counter ganks is much harder since them ganking you, there will be more enemy champs there.

I prioritize it that the first time I go back to buy items, I also pick up a ward or two depending if the amount of gold I farmed covers it.
Generally I use it for watch on the dragon, but other spots I use them include the golem/lizard spawns at the bushes and other chokepoint bushes such as the ones on the side of second-mid tower.

Side note: Even though I main as Nidalee, her traps don't actually provide sight when unsprung, which makes them less convenient for your teammates. While I can keep an eye on my trap locations, my teammates probably can't.

So yeah, wards do help win games. I can't begin to think how many times I've managed to avoid ambushes due to it.