Start with getting your Doran's Blade and Health potions and just grind minions until you have 700 gold, then channel back and purchase Sheen, (This will get soem of the extra damage Trinity Force offers early game). It's 100% up to you whether or not you engage during this time period, if you do engage and you win it means you get Sheen faster, however avoid dying at all cost the wait time and walk back time will put you behind in income and exp.
Once you get Sheen you then want to keep grinding gold for Trinity Force. You have the extra damage to be able to play with your support and take almost any fight bot, (almost, anything can happen) Make sure you engage and get kills as this is one of your only ways of getting marks, on that note pay attention to where your wolf mark is as having scuttle or blue rocks or red frog as your jung mark could potentially get you a free mark.

By now you probably have your Trinity force and Stormrazor. This is the point where it's ok to stray from your path bot lane and help teamates out with ganks on mid, by now you are strong enough to take most fights as long as you have a tank nearby or someone else who can take hits for you. Remember you're going to build Bloodthirster so you want to grind minions and camps when you get the chance, although if you're consistently killing your opponents this shouldn't be a problem.
After you build Bloodthirster you can build either Runaan's Hurricane or Beserker Boots. If you aren't doing much damage with basic abilities, fighting someone with more range, or someone faster than go Beserker Boots; However if you are doing a lot of damage in fights or have 8+ marks go for Runaan's Hurricane since you already get a movement speed buff from Trinity Force and haveing 8+ marks increases your range from 500->600.

You want to build Wit's End last, Wit's End's passive FRAY has bennefit damage from Lifesteal which you have from Bloodthirster. This should allow you to win almost any fight.