Playing TF well, is hard. The best way to play is to take w first for mana sustain, then max q first, the biggest problem is positioning with TF. You have to be able to hit multiple targets with your q. That means getting a feel for how your q will spread. so you need to adjust your distance based on that. I typically run magicpen/armor/mr for reds/yellows/blues and movespeed quints. MS quints are so important on TF to achieve your goal of positioning. Also they help with the lack of escape since once you get lichbane you'll be pretty fast. The biggest problem with a lot of TF players i see is lack of map awareness, because to use his ult you have to have great map awareness. TF skillcap is pretty high, I can play TF and not be bad, but I'm not a great TF. Basically early game you want to keep your w on cool down so you're constantly regening mana or harassing enemy. You gotta memorize the order of your card rotation. Best way to do this is to maybe just make a custom game and practice on minions till its automatic, because if you can't pull a gold card when you're getting ganked or pull a red card in a team fight then you'll be a bad tf. The high level TF meta is difficult because you have to chain things together really well, like at level 4 I typically take stacked deck so your every fourth attack you deal extra damage so the auto attack before your 4th you wanna pull a gold card if you can get in close or a red card if you a little out of range but your opponent is near minions. Then you stun/slow them move in(cuz your fast with ms quints) then you q/auto attack them for lots of harass. So why not wait for the 4th attack to pick a card? I've found that because TF gets what appears to be a tutu of cards around his waist when stacked deck happens, so since the other player can see this if they are smart you will never get close to them if you're picking a card and have stacked deck up.
As far as items you can go a couple ways, depending on how your lane is going. Sorc boots are usually a good idea, usually if you're trying to kill i go sheen next, or if i'm gonna farm i'll take blasting wand. I see some people take DFG, but I think lich bane does what TF wants to do more than what DFG does. I mean you can rush it if you owning your lane, but like for ganking other lanes early sorc boots and sheen is better because you're typically not initiating the gank with tf your following up and dfg is not as good for this. Also TF passively gain CDR from his E which you won't max untill last but still I just don't think that DFG offers enough for TF to be really interested in it. Because at level 18 you're going to have 15% CDR from stacked deck and 20% from blue buff, because blue buff is awesome on TF, and 4% off of masteries so that gives you 39% CDR and any more is just a waste unless for some reason you never get blue buff, which shouldn't happen.
So just quickly a word on team fights. You're not really an initiator, you burst, you reset, you burst again. red card if you can't reach anyone important, if you are in range of a carry gold card them. Your range is huge, like Q has range of like 1100 so use that. One of the best things TF does is play clean up after a team fight, so like maybe their carry is trying to escape just after a team fight through the jungle after baron, the carry is probably going to run mid, assuming he ran towards wraiths so you can cut him off by ulting into the bush next to wraiths. Probably you have the kill right there, but if the carry knows whats up he really can only keep running towards you, towards small golems and you be able to catch up, or turn around into your team.