I don't play Leo, but I got from low silver to G1 playing predominantly support/jungle last season (G3 currenty).
First and foremost, you cannot win your lane if your adc is junk/doesn't play adc. You can save your adc from death, harass enemy adc, ward thoroughly, roam/ping, etc, but the support is only half the lane. The other half is the adc following up on your plays (and vice versa with a good adc). Furthermore, if your team doesn't notice the vision you provide, doesn't follow up on your engages, re-engages after you disengage, or just flat out sucks at the game, you cannot win games as support. Again, this is a team game, and unfortunately, sometimes you just lose.
As far as laning goes, there are 2 general zones that are very important as support regarding positioning. I've attached a crap pic to demonstrate. Zone 2 is where people like blitz, leo, and morg like to hang out. It provides cover for their abilities and can force the enemy to blow their trinkets in the early levels, leaving jungle paths clear for your jungler (which you should communicate). It's important to maintain control over this zone as it can turn the tide in a trade if not warded, as it interrupts auto animations and forces "spell chasing" (when you use something like janna W on an opponent who runs into unwarded bush, you end up chasing them by default unless you command otherwise).
Then there is zone 1. This is where I like to be, as I main poke supports like karma and sona. If red team is trying to control zone 2 while hiding in the bush etc, then blue team can simply ignore this tactic by hovering near river in zone 1. Thus, you're out of range of support in zone 2 and are free to shove lane quickly, forcing support to leave zone 2 and back up towards their tower. If zone 2 support leaves bush, you rotate back towards zone 2 to incentivize enemies to go back to zone 2. If support leaves zone 2 aggressively, in front of minion wave and ready to hard-engage, you simply exit via river. You may lost 2-3 cs this way, but you'll save yourself 2 deaths.
The real advantage to zone 1 is control over enemy adc. While blitz may be free to sit in bush for the entire game, graves has to be in lane in order to cs. This leaves him open for things like sona Q/karma Q from zone 1, and he cannot do anything about it besides lose cs or hard engage. Hard engaging with low HP is foolish, and this is where zone 1 thrives. HP wars are crucial early levels, and if you can chunk your enemy HP to about 50%, they can no longer consider hard engaging. I cannot tell you how many times I've won lane simply by hovering near zone 1 and hitting Q as sona while the enemy blitz/leo/morg sits in bush waiting for a chance to all-in that never comes.
Obviously, there is much more to laning. There is more detailed aspects of positioning, there is champ match-up (both adc and support), there is jungler match-up and what to expcect from your jungler (no ganks from WW pre-6, etc), mid roaming potential (ward hard if enemy is LB/kat), syngery with your adc, drag control, wave management, etc. I cannot type all of my experiences here, as it would be a frigging novel. I mentioned zone 1 vs zone 2 as this simple concept alone has pretty much carried me to gold regarding my supporting. It is also worth it to type out to your adc that you plan on utilizing one of these zones. I often tell my adc "hover near river to avoid blitz in bush and we win lane via poke", and they listen.
