WizLiz made a pretty good description of what to buy, how to launch your spells and how to kill monsters. But being in the jungle with Nature's Prophet is more than juste killing creeps.
Remember than this hero got one of the most powerfull Dota 2 skill : Teleportation. Which means that he basically can go everywhere in a few seconds. That is what makes him such a good Jungler or an even better off-lane hero.
With a typical jungler you will usually kills creeps until you are ready to get out of the jungle. With Furion, don't forget that your role is also to help your mates killing on their lanes. At level 5 you should have 1/1/3, to be able to teleport on a lane, kill a hero (using sprout if necessary) and TP back to base (don't forget to always carry a TP with Furion, this is true with all heroes but with his teleportation you may forget that this is a life saver).
If you want to be a good jungler with Nature's Prophet, observation of the whole map and communication (if possible) are essential. If you see your team-mates ganking, and if you think a teleport would help the job, or that you can finish a fleeing hero by teleporting on his path, do it. That is what makes Furion so powerful, even during the first 10 minutes of a game.
Remember : don't get stuck in your jungle, that would be a huge waste with Nature's Prophet.
Edit : Would have been better as a comment of the previous answer, but I can't comment yet.
Edit 2 : You also must use teleportation in a defensive manner. If your offlane is being chassed under his tower, a TP + sprout can completely change the outcome. I suggest to watch some replays, especially with AdmiralBulldog, who is part of Alliance and the best Nature's Prophet player in the pro gaming community.