Level 30 is the max level for a Summoner, but how much XP does it take to get there? About how many 5v5 matches does it take to get that much (assuming 50% win/loss ratio)?
According to the wiki, it takes 40083xp.
Also from the wiki:
Assuming an average XP gain to be about 110 XP per game, one can reach summoner level 30 within 365 normal games.
Adding to the previous response, you can purchase XP boosts from the store to help you gain more points per win if you are really interested to get to level 30 faster. Please understand the competition for the most part have won about 150 games to level 30 so the faster you progress the less time you have to develop the necessary skills to play at the higher level.