Hey!
Take a look at this short explanation (it is from the official LoL FAQ page):
You will be placed in the low priority queue for 5 games. If you continuously leave, the low priority queue timers increase from 5 minutes per game to 10 minutes per game and then capping out at 20 minutes per game.
As mentioned already by @ Fruxo- You must play the required amount of games to lift the low priority queues. You must wait the entire time in the lobby otherwise it'll reset the timer and evidently have to sit through it again. Increases in time the more games you leave after the fact.
I'd suggest avoiding leaving in-progress games if you can. Or if you're prone to bad internet, sort that out first to avoid any disconnections.
If I recall correctly it should be 5 games in total to get out. However, the more games you leave, the higher the queue will become and it's more than likely you'd have to play more games if you want to get out of that queue.
So if it gets up to 10 minutes would I have to play 10 games? Also does this have to be all in one sitting? And once I do play the games does that get me out of the low priority queue until I start disconnecting and/or dodging again? Sorry about all the questions I just really want to get back out on the rift and prove that I am a valuable summoner!
Don't know about the games increasing per time. I just know that continually dodging/leaving games will contribute to the time increasing. They do not have to be in one sitting, you just have to play games at any time. Once you finish playing those games, you'll be out of the queue yes.
Take a look at this short explanation (it is from the official LoL FAQ page):
You will be placed in the low priority queue for 5 games. If you continuously leave, the low priority queue timers increase from 5 minutes per game to 10 minutes per game and then capping out at 20 minutes per game.
Hope it makes everything clear. Good luck!
I'd suggest avoiding leaving in-progress games if you can. Or if you're prone to bad internet, sort that out first to avoid any disconnections.