1. Ward-if your support can't/won't, don't hesitate to pick up a pink ward in order to check for enemy wards so that you can gank or pick up dragon (and later, baron). Once you clear the ward, wait a few minutes and make sure your lanes are pushed before you pick up dragon.
2. Don't tell your team that it's your first/second/etc ranked game, they will likely put you off as bad and blame you if you guys are losing.
3. Stay cool. If you make a mistake, admit it and remember it and try not to make it again.
4. Keep your objectives in mind. Control of towers, dragon, baron, red buffs, blue buffs, map control. Gold is an important factor, so dragon and baron and kills are helpful, but don't suicide 1v4 while they're at dragon because that will just put you further behind. Take a second to think about who is MIA and whether or not you can win before you dive people. Don't chase bait.
5. Praise your team for doing well. Even just a "nice gank" can go a long way in making people feel comfortable.
6. If you're mid, remember to gank and help your team or they might fall behind. If you jungle, make sure to gank and help your team or you WILL fall behind (though with the new Season 3 changes this may change). If you are top, know whether or not you can kill the enemy, make sure to farm and then help your other lanes, because you will have a lot of gold. If you ADC, make sure to farm and control dragon, killing an enemy only gives as much gold as 13-14 creeps, so you can win the earlygame just by out-farming them. If you are support, WARD WARD WARD. Philo Stone for supports, and prioritize wards over items in general. Pink wards allow you to take out enemy wards, so watch where they ward (especially if they buy pinks because you want to put yours down after them to kill theirs first). Pink wards and other wards wards wards wards on dragon and baron. If you are purple team, a ward right in the opening to dragon will let you see if they warded inside his nest. (Or, as blue, in baron's nest.)
7. Take a break after every game to stretch, make sure to stay well-fed on a balanced diet and hydrated so that you are mentally able to think about the game.
And last, getting better will come with time as you learn how to build in different situations and learn more about the strengths and weaknesses of all 107+ champions in the game and how to outplay and win against them!
And have fun, psh, that too.