Some really good answers here, so I'll add what hasn't been said yet:
The best junglers for learning the role are Warwick, Fiddlesticks, Yi, and Vi right now (Amumu would be but he's weak at the moment, Nunu can be tempting but he's actually an anti-jungler that's supposed to crap on the enemy jungler and if you don't do that he's mostly useless). Warwick just farms to 6 and then ganks with his ult, Fiddles can sustain for days and gank decently and scales well into lategame, Yi farms up into a monster (although you can also gank if they're really pushed), and Vi is just all-around strong and pretty mechanically simple for a 6300 champ.
Build
every game until you're comfortable ganking, and then
instead depending on how much you want to gank. Get
if there's an enemy champ that goes invisible, or if you're being invaded by the enemy jungler.
Pulling off good ganks takes a lot of practise. I'd recommend looking at the lane before you commit to the gank, check everyone's health and mana, levels, etc. This is where youtube really comes in handy, find a youtuber who talks while they play (Foxdrop is great) and you'll pick this up faster.
If a lane is losing badly and crying for ganks, just mute them and camp another lane. Once they're 0/4 or whatever, getting them a kill will just increase the amount of gold the enemy gets for killing them. Try to get the other lanes ahead to compensate. Junglers take a lot of crap from the laners because a lot of laners don't jungle and don't understand what a jungler can or can't do, so they assume that because you're not magically 50/0 before you get your buffs done you're trolling.
Keep an eye on the dragon timer on the scoreboard (press Tab to see it). Dragon control wins games.
Don't play the invade champs (Nunu and Shaco) until you're really good at jungling. And even then, just play them a bit to learn invading, but invading is a really bad idea what with how the jungle is right now.