Roaming has become a popular addition to the metagame strategy, wherein one player does not lane nor jungle, but rather simply moves through the jungle/river to initiate ganks on lanes from level 1 and onward, until the teamfight portion of the game begins.
A roamer essentially guarantees that you're either running a solo lane, or two solo lanes if you have a roamer and a jungler. I've also seen a double roamer game played, though this tends to be less effective as enemies who are wise start playing defensively and reduce the effectiveness of your roamers, which put them behind in both CS and levels.
The qualities of a roamer can vary, but the general requirements are that they are mobile, can do burst damage, and have a strong stun or position altering (push, throw, etc.) ability. Taric, Evelynn and Alistar are all very popular choices for roaming. I've also seen Sion and Blitz play roaming effectively, but they were both out of a lack of a jungle spot on the team and normally suit better in a lane.
This strategy is similar to the "double jungle" mindset in that you get three solo lanes, with the exception that there is extra pressure on getting early kills to succeed. A definite risk vs. reward tossup, as successful roamers will quickly catapult your laners ahead in level / CS as well as demoralize your opponents, but unsuccessful roamers will fall just as far behind due to the lack of their presence in the laning phase.
Playing other champions really gives you a feel for how to handle situations. It is important to know what your champion is capapable of and what they are capable of. I can offer some tips though.
Watch your map: This one is the most important, always watch your map. When more than one person is missing on the enemy team you should be moving to a safe position. Make sure you know where your enemies are or where they were heading last seen. Keep the map scouted and when 3+ people are missing you should be trying to bunch up aswell. If theres 3 or more people missing and you're pushing a lane deep then most likely they are coming to kill you.
Know your role: If you're the tank, be the tank. Protect your squishies, stay close to them and protect them. They are usually your carries and thats how you will win the teamfights. Rally your team, don't be afraid to boss them around. "All push mid" "Group up". Late game power is all yours as the tank, you engage, you chose where and when to engage and where to push. Without you your team is pretty useless. If you're the carry, stick to the tank farm within moderation and keep an eye on the map. You're who they're disappearing to come kill. Stick to the brush when teamfights engage so they can't come in and just ice you and run away. Don't reveal yourself till some spells have been cast and they have already begun focusing another less squishy player. If you're support, keep the tank alive and watch your squishys.
Don't wander: If its late game and you're all level 18 its time to be a team, move together, stay close. Don't over extend and wandering also involves watching the maps. If the enemy team is pushed into their base and fending off super mionons go steal their camps, but just always farm in moderation and never over extend.
Know your enemy: Once again coming back to knowing the champions. If you're the tank and the majority of the enemy team damage dealers are ability power then stack magic resist, if you're a carry and a majority of the enemies are tanky high health grab a madreds and tear them down. Don't trust mobafire 100%. No build is gaurenteed every time. I say this all the time, LoL is dynamic and should be played as such. Build your build around the enemy team and what your team needs from you.
Also a side-note worth mentioning, once you can buy tier 3 runes build some pages for your favorite champions. Try to make ambiguous pages that can apply to for example all AD carries or all tanks. Some good purchase starting points are armor seals, armor pen marks, and magic pen marks. You can use them for basically any character.
Best Answer
A "kill lane" in bottom is a different strategy of winning your lane. A very general definition of "winning your lane" is that you have generated more gold, experience, and map presence than your lane opponent(s).
In bottom lane, the standard strategy is to get a lane with high sustain and ranged attacks which reduces the potential for being harassed and reduces the impact of harassment by having heals, shields, or other damage mitigation. This is essentially a "farm lane." Your goal is to get as much creep score (CS) as possible, and hopefully some kills along the way to bolster the amount of gold and experience you receive (as well as reduce the amount your opponents receive).
By contrast, a "kill lane" is one where the focus is on killing your opponents. Usually this is accomplished by having two characters with crowd-control, at least one of whom can also deal fair damage. You would normally pick a kill lane to counter a farm lane, which often has at least one character considered "squishy" (low hp, armor, and/or magic resist), making the kills easier. Commonly chosen combinations are Jarvan and Leona, Sion and Nautilus, and (more antiquated due to Taric's lack of damage) Taric and Sion. The reasoning is that each of these groups either have a large amount of CC, burst potential, tankiness (so they can tower-dive and are hard to get out of lane), or a combination of all three.
Sion makes a great choice because of his stun and burst potential. You can also build AD Sion and rely on your extra damage from Enrage in combination with your stun. Leona has fair damage when paired with someone else because of her passive ability, and also has three crowd-control mechanisms at level 6. Jarvan is a good choice with her because he has two crowd-control measures of his own and has similar mobility. Nautilus is prized for the same reasons as Jarvan, but his passive gives him an additional crowd control opportunity (though he lacks the same damage and farming potential as Jarvan).
While it's obvious that you get gold and experience from repeatedly killing your lane, those numbers become less significant as the game goes on (assuming you're even successful). Additionally, at first glance, it seems like you wouldn't be able to generate as much gold for your lane as a strict farm lane could (given the diminishing returns of killing the same player over and over). However, there are important indirect results of the kill lane: