Nature's Prophet is amazing in any lane with any hero but since you will be carrying going to safe lane could be considered. If any of your team member decides to jungle taking that solo sidelande is no-brainer since dominating lanes is that easy. When you got to your lane, just start farming. Last hit properly and you will be fine BUT since your Sprout will trap enemy for 3 seconds at lvl 1 using it to setup easy fist blood should be prioritized especially when duolaning. "They have tangos" you say, who cares? 90% of people will start panic while they're sprouted so use that advantage.
As soon as you got lvl 6, spam your Wrath of Nature wherever it's off cooldown since you will get tons of gold from it, also sometimes you will even lasthit some heroes if you're lucky enough. As for the items you should already have threads and maybe some kills. Since you leveled your Treants properly now you can push hard. Destroying your lane's tower shouldn't be hard and as soon as you did that (usually before 10 minutes) get your Hand of Midas. After that you should just teleport to another lane, and destroy tower there.
So, you have pushed all 1 tier towers and got some kills. Now you should at least gotten Malestorm with part of Desolator and it's time to own. If you see any fight, even 2:2 one, just tp in, Sprout your target and enjoy a free kill. Finishing off low hp heroes from across the map is so satisfying with your ult.
As soon as you got all your desired items (I strongly recommend Daedalus) you can solo Roshan with no problems. Get Smoke of Deceit in case they have wards, get to Roshan's cave, use Sprout to create Treants and let them tank all the hits. After a bit of rightclicking you should kill Roshan without taking any notable damage.
After you met Roshan and got everything you could possibly think of using your ult and Hand of Midas - just end it. Now you can kill almost anyone 1:2 and push all lanes by tp'ing from lane-to-lane destroying towers in no time. So just get top or bottom barracks and regroup with your team on mid. One hard push and it will be most likely over even if their carry is fed because you will easily do 300+ damage and add critical strikes on top of that.
One last tip. NEVER jungle with Furion. When I see people jungling with him it makes me so sad... It's like buying a Maserati and driving some Honda instead. The kills you can get from your Sprout, the gold you will get from early pushing, the xp you will get from creeps is just too much to miss. So yeah, NEVER EVER jungle with Nature's Prophet.
Thank you for reading this guide. It is my 1st guide and based only on my experience with this hero, hopefully you will find it useful and it will help you out getting gg's and enjoying full potential of Nature's Prophet. See you guys later!