Trollz will be Trollz

This may come as quite a shock to you, but not everyone who makes up the League of Legends user base is going to be a nice, intelligent and helpful person.  In fact, a large portion of the player base would, at first glance, appear to be made up of 8 year old's with pleasant Summoner names like “Xplosiv3D1arrea” and “EyeH8Jews”, and so on... and mentalities that fit their names oh so perfectly.  There are lots of different types of these people playing LoL matches every day.  I will list some examples and the proper response when each one shows up in your game.

1.      The Feeder—Chooses to, for a variety of different reasons, to continually suicide into the enemy team.  Will sometimes blame others for their deaths even though it was very obviously on purpose.
Response:  Ignore them, try to play the game as best you can.  It isn't likely, but you MIGHT be able to win anyway.  If not, surrender at minute 20 and Report them for feeding.

2.      The Harasser—Whether provoked or not, The Harasser will spend all game shouting profanities, racial slurs, noob, and the like.   Usually they target one person.
Response:  Ignore them, try to play the game as best you can.  There is no telling whether or not this person is good at the game so you might when, you might lose.  Report them after the game for harassing.

3.      The Troll—This player is not here to actually play the game at all.  They are just playing so they can ruin someone's day.  They will spend all game bitching for no reason, calling people out for being bad, build items on champs that make no sense (AP on Garen for example), and/or general game disruption.
Response:  Ignore them, try to play the game as best you can.  Report them after the game is over.

4.      The Leaver—The most irritating type, but also the easiest to deal with.  At least you don't have to ignore these people, as they are no longer in the game.  It could be the disconnected at level 1, or maybe RAGE quit some time during the match.
Response:  It is not impossible to win a 4v5, I have done it several times.  It does take good teamwork though.  But if you decide you give up just because someone else quit, then you are just giving away a victory that could have been yours if you kept on trying.  Keep playing, try to win.  Report the leaver after the game.

And there are a lot more where that came from.  Did you notice the trend?  Just ignore them, try your best, strive for victory under slightly skewed conditions, and then report the griefer after the match.  Riot has recently added a new system, The Tribunal, to help with all these griefers in our games.  By submitting a report every time someone fails to uphold the summoners code, you are adding just a small part to the cleaning up of the game as a whole.  And you can do another small part by voting to punish those that deserve it in The Tribunal.  But the biggest thing that you could do to prevent these attacks, is just don't react to them.  Every single one of these griefers is only doing it to get some sort of response.  And if they keep getting a response they are going to continue to do it.  Riot gave us a /ignore command for a reason.  USE IT.

As a side note:  Just because someone is not doing well, does not mean they are a griefer.  Maybe they are new to the game in lower level games.  Maybe they are trying out a new champion and can't seem to get the hang of it.  Don't be snotty about it, but ask if they are new to the champ or game.  If they say yes, then give them a break.  Suggest websites with information, give small pieces of advice, or (I cannot stress the first word in this enough) CONSTRUCTIVE criticism. Don't just tell them they are bad and should quit.  If you know how he/she could be doing better, tell them in a polite way.

You will always get people on your team who are not at the same skill level as you, or that just do not understand certain game mechanics, but that is no reason to start raging yourself.  Don't become one of the griefers.  Unskilled players and griefers will always be a part of the game, but you can do a lot to prevent the numbers from getting outrageously high.