Jungle is a difficult role for many people because its emphasis is on the strategic aspect of League instead of the mechanical aspect. When you're laning, you're really only concerned with the mechanics of your champ, last-hitting, harassing, etc. In the jungle, mechanics are an afterthought (i.e. learn the correct skill timings to clear camps, lather, rinse, repeat), but decision-making is integral to your success. You need to be watching the minimap so you can plan your jungle-clearing path to end up in a lane that's ready for a gank. You'll have to choose which lane will benefit the team most from your help when all your lanes are doing poorly. You'll need to use your Smite wisely so it's earning you the camp buffs when you need them, and time it so that it's available when your team is taking Dragon or Baron. You have to pay close attention to your teammates pings and chats so you know what's warded, who's in or out of a lane at any given time, and who's in most dire need of your help. And that's just a basic summary.
Since you specifically asked about wards, I'll offer some basic advice. In short, don't worry about them. Just plan your clearing route to put you near a lane that's pushed, and go in for a gank. Even if the bush is warded, try to gank anyway. People tunnel-vision ALL THE TIME... just because they put wards in the river and the tri-bush doesn't mean they're paying attention to their minimap to see you passing by the wards. As other posters mentioned above, the Sweeping Lens and the Smite buff from the Raptor camp are both great tools for avoiding wards. The Sweeper not only reveals wards, but disables their vision so you can freely pass over them to gank. The Raptor buff will alert you with a bright pink light when you've been spotted by a ward, so if you've got the buff and you go to gank and no pink lightbulb appears above your head, that means the enemy team CANNOT see you.