Let me start off by saying how tiring it is playing the same characters day in day out. It's fun to try something weird and have it work. AD Annie is a very similar build to this one.
You're looking at Heimer's skills right now and saying to yourself, "Wait, none of these get any better with attack damage." And you're right. They don't. Turrets don't use AD either, don't worry about testing it.
So you're wondering, why do it? Because it's fun.
Start out with a Meki's Pendant, HP pot, and Mana pot. Be mid.
Your match starts out the same way any Heimer mid is: cautious.
Don't go past the middle if you don't have to. Always have at least 1 gun by you. Last hit, for the love of god.
When you get to 955 gold, go get your boots and your tear of the goddess. Teleport back up to mid.
Save up another 1550 or so and get your vamp scepter and your manamune - your first source of true AD.
Etc etc. Just keep mid nice and farmed and have your jungler tear **** up.