So, here's a guide on how to play Furion as an annoying piece of **** (in non-pro games where [most] everyone knows what he or she is doing, since that's where most of us play). It is a work in progress, and I will build the guide off of comments and other nice things like that. First and foremost, I'm going to discuss Furion's role in the team. As Furion, you should be incredibly busy throughout the game, performing tasks such as ganking, pushing, and being an annoying piece of ****. Early game, you should be the jungling, helping in ganks, and stacking/pulling creeps for the easy lane. Mid game, you should be focusing on pushing first, ganking second, and farming should come with both of those. Generally speaking, Furion doesn't have the skill set to be able to carry late game, and does not scale well by any means. However, his farming potential is absolutely ridiculous, and if left alone, can take down all tier 1 and 2 towers within 15 minutes and carry. More on how he does these things in the skills section. Also, another reminder: remember that a guide is never the only way to play a certain hero; make sure to adjust a build to your tastes if something in particular doesn't work for you.
Your "Q" skill is sprout, which spawns a ring of trees around the point where you cast it. Sprout's an incredibly useful skill, as it lasts 5.25 seconds at level 4. Unfortunately, it's pretty easy to counter when the opposing team wises up and carries Quelling Blades or more Tangoes. Additionally, skills such as Windrunner's Powershot and Beastmaster's Wild Axes, which remove trees, pretty easily render Sprout useless. However, for early game, it's an excellent tool to use in ganking if you cast it on an enemy hero without any of these abilities (or decent knowledge of the game). Furthermore, the trees themselves give vision where they are cast, so if cast in a bunch of trees when a fleeing hero is attempting to vision juke, they will be revealed if in close proximity to the Sprout. Also, Sprout is a targetted spell, but you can also cast it uphill if you lose vision of the intended target (much like Crystal Maiden's Frost Nova). Even more awesome and annoying, you can cast it on yourself, and the enemy will lose vision of you so long as no enemy creep or hero is also caught inside. If you have the option enabled, you can just double tap "Q" and it will automatically sprout trees around yourself. Don't be overconfident that you're safe inside a Sprout, however, since heroes like Pudge can just pull you right out without vision. More on how Sprout supplements your other skills later. You don't need too many levels of sprout early game, as most people will be carrying Tangoes, and you'll be jungling anyway.
Your "W" skill is Teleportation, also your annoying pushing ability. It allows you to teleport anywhere on the map, so long as it was previously explored by your team. The excellent thing about this skill is that it's not only global, it doesn't go on cooldown until you complete the teleportation. So, let's say Slardar is sprinting at you. You panic, and try to teleport home. Slardar stuns. Teleportation isn't on cooldown, so you just teleport home again and laugh as he rages. With this skill, you basically never have to use TP scrolls, unless your team is desperate for a helping hand for counter pushing. This should rarely be the case, since if the enemy team is pushing one lane, you should be pushing another. You can double tap "W" and it will automatically teleport you to your fountain. Otherwise, just click on any place on the map. You can often Sprout yourself and safely teleport home. At level four it has 20 seconds of cooldown, hence making you an annoying piece of ****.
Insanely annoying skill. You cast it on a bunch of trees, which proceeds to turn into walking annoying pieces of ****. They're your main pushing tools; have them attack and tank the tower while you get in some hits for yourself. If you don't see any trees in the immediate area, and are too lazy to find some, simply Sprout a random area on the ground, Nature's Call on it, and have some more trees. These treants are also your main jungling tool early game, used to tank creeps while you chug clarities to sustain your mana pool. At around 40 second before the game starts, cast Nature's Call on the trees near your fountain, and send one each to scout rune for lulz. At four seconds after the game starts, stay in fountain, cast another Nature's Call, regenerate mana in fountain, and proceed to jungle with full mana and two trees to tank. Max this first as you shall be granted excellent pushing power.
Wrath of Nature
Furion's main farming tool, besides pushing down towers. It's a global ability that bounces around, hitting all non-friendly units. Note that the first target it hits takes the least damage, and the last target it hits will take insane damage, especially with Agh's. You want to use this ability when you see a near-full creep wave in each lane, maximizing the number of targets. At level 16 with Agh's, you can be getting 800 gold with one ult if you get lucky. The ult should be used at every cooldown, assuming the condition above has been met. Remember, if you want to ks a hero who is on the other side of the map, don't target him with your ult unless you're in danger of losing vision of him. Instead, cast it far away from the intended target, maximizing damage dealt for more lulz.
Ring of Basilius
Great item for jungling, increases mana regen needed to cast Nature's Call, and increases armor for your treants so they don't die as quickly. Great item for jungling and pushing.
Grab as many of these as you can after RoB. They're great for your jungling session since you won't be getting hit. Disregard the tangoes suggestion in-game, since you should let the treants do all the tanking. Because you're a relatively squishy hero, you don't want to be at half health when your easy lane needs help.
Situational: Animal Courier
If you end up with a ****py team with no support, it is upon Furion to buy the animal courier. Your farm will be better than anyone else's, anyway, so no need to worry about that extra gold. This really shouldn't be your job, though, in semi-serious games.
Situational: Observer Wards
Similar to the cause of buying courier, being a man and stepping up to buy wards benefits everyone. Again, do this only if you don't have a willing support.
Really, you don't need anything else, and Furion has good enough base damage where he deals painful autoattacks. Also, the only real useful footwear for attacking towers. BoT is useless due to Teleportation. As for Phase Boots, you shouldn't be doing a whole lot of chasing, because in ganks you should be teleporting behind the enemy hero, cutting off escape with Sprout. Arcane boots aren't really necessary, since you have plenty of mana regen both with RoB and frequent low-mana cost teleports back to fountain, and the same goes for Tranquils.
Makes your ult more powerful, increasing damage and bounces, further increasing farm. A lot of people argue against getting Agh's asap, but it makes your ult a really useful ability ingame, able to deal massive amounts of damage prior to a team fight, farm gold, and counterpush.
Makes your tower killing ability increase greatly, while increasing your ability to deal massive damage. This item really allows you to take towers down quickly while your treants tank.
Situational: Hand of Midas
Only if your team has no hard carry, and you feel like farming even more. Otherwise, getting Agh's first is generally the better idea. Too often do people get this item and forget to use it on every cool down. Use Midas on high level neutrals at every cooldown for exp and gold. If you choose to go the Midas path, go Clarity -> Clarity -> Gloves of Haste -> Boots of Speed(you can skip boots) -> Hand of Midas
If you don't feel comfortable pushing towers, take Shadow Blade. You push, you see enemy heroes coming, you cast Shadow Blade, you run off, and you teleport home. Note that the invisibility isn't actually dispelled when you cast Teleportation. It only wears off the after the teleport is complete, so you can cast Teleportation while Shadow Blade-d.
Should be self explanatory why these are situational.
This section depends on if you're serious, or if you are lawling at the other team and are dominating them.
These are the serious items, as you really shouldn't be playing the carry role, but should be using your farm to gain utility for your team. Orchid against spell-dependent teams, Shiva's for a great aoe slow/nuke, and Guinsoo's for a great all-around disable.
Team needs a carry/You want more kills:
Self explanatory, increase damage and great lawlz when you're farmed and one hitting ancients.
The key to playing Furion is to establish an aggressive global presence as early as possible. While jungling, coming out and casting a quick sprout for First Blood makes the enemy scared of getting ganked, making them play more passively and allowing the lane to be easier for your teammates.
To conclude, Furion is an extremely powerful hero who is able to put intense pressure on the enemy team with global ganks and pushing. Replays will be up soon, and please add comments to share your opinion on your own builds. Thanks for reading!