Ip (Influence Points)
You will receive an certain amount of influence points after you finish a game and you can you the Ip that you have collected to buy new champions, runes and additional rune page(Other Section in shop)
If you are still under level 30, you will also receive experience. For both Ip and Experience, if you win you will receive more points.
First Win Bonus
Every 22 hours there will be a First Win Bonus which give 150 Ip extra to your account.
Note: that the grey area of +46 Ip is an Ip Boost which you can buy from shop by using Rp
Unlike Ip, you only can get Rp by buying it via shop. Rp can be used to buy champions or skins(which make your champion looks better than the opponents). You can buy via shop by credit card, sms or paypal. If you don’t have credit card, you can go to you local shop(click here to check League of Legends announcement on availability)
In League of Legends, you will start at level 1 when you create a new account and the max level is 30.
Every level will give you a point in Mastery, open up new summoner spells and once you reach level 30, you will be able to play on ranked game (more on ranked game later)
So here is the mastery screen and it showing my solo top Teemo page (taken from solomid.net by TheRainMan)
As you can see there are 3 different mastery trees (Offensive, Defensive and Support), all mastery will affect your in-game stats.
When you gain level you will also gain extra summoner spells. Every player will be able to pick 2 summoner spells to be used in game, majority of players will pick Flash, because of its function.
The first 2 rows are available from level 1, while the rest will become available as you gain level.