First off, this is a build the requires a lot of experience with tf. You're going to need to be able to lock in cards you want correctly almost all the time, the gold card is the most important. Blue card will be your last hitting tool / harassing tool. You also need to be able to use the hextech gunblade's active. This build is heavily centered around the Hextech gunblade because it is a great hybrid item for TF due to it's active, spell vamp, and life steal.

You want to get as many last hits as possible, try harassing them with Q at level 1. At level 2 last hit with blue cards to keep your mana up harass them with Q, another way to harass is to gold card + Q + auto attacks. If you get them lower than half health, lock in gold card, flash in, gold card + Q + ignite + some auto attacks should get them killed. If not, they will almost be dead and you will have free farm + hits on turret until they're back. If you're getting harassed a lot, just do anything in your power to last hit as much as possible. Get your jungler / roamer to come gank and get your dominance on the lane.

Once you hit 6 you should teleport in and see if you can get a kill top or bottom, only if you're wrecking your lane though. Once you have trinity force your damage will become drastically higher and you can wreck most squishies and tanky dps. During this point, the only card you're going to need is Gold Card for team fights and your Q. If you're low on mana just use blue card on minions. If you're able too, get the blue and red buff and you can kill almost anyone, as long as it's OK with your jungler that you can take them. You should be able to lock in gold cards consecutively as soon as the cool downs are over to lock in kills. Kite enemies as much as possible. When you teleport in, before you teleport make sure to lock in yellow card so you can stun them right when you get there

This is when you truly shine. You can port in on overextended squishies, gold card, Q, and use hextechs active along with some auto attacks and they'll be dead in a heartbeat. In teamfights make sure to not get initiated on. During the teamfights focus their carries / supports / tanky dps. You will do massive damage on all of them. Help your team as much as you can too. Once you have 2+ hextechs your life steal, damage, and spell vamp will be so high you'll be able to leave teamfights, use your wild cards to get some health back, and go right back in.

Just make sure to play smart, and help your team. Make sure to use your Hextech gunblade, Good Luck!