Usually most people level Double Up first and then the other skills, I personally level up Impure Shots first and foremost, you'd be amazed how much it increases your damage output in a 1vs1 situation, not to mention people will usually underestimate the amount of stacking damage you're going to get from it with each hit (about 40 extra damage at 4 stacks with Lvl5 Impure Shots).

But yeah, I usually use Make It Rain and then fire at least 2 shots at whoever is in my lane for harassment, this will make them both towerhug and make them think twice about getting that low HP minion.

As for items, mine go:
-Boots
-Brutalizer
-Pickaxe
-Survivability item (Banshee's if the enemy team is heavy on mages, or just Phage for the HP + slowing).
-Finish Infinity Edge.
-Bloodthirster(s).
-Guardian Angel if needed.

Go with what you think you'd need the most depending on your situation.

Cleanse/Ghost

9/0/21

QWQEQR - R>Q>W>E

Dorans Boots BT Banshee

Q
Abuse strut to land safe empowered Qs during laning but don't be afraid to trade if you will come out on top.
Spam it on the tanks mid late game

E
Use it to check bushes and behind walls
Don't listen to the sillyness of farming with make it rain, Q and autoattack gives you 80%+ of the creep kills easily.

R
Use it to farm/push a lane before going to buy.
You can use it to snipe kills and get runners but its not as good as it used to be at that.
Unless you get a perfect initiate/opportunity to start the fight with R don't use it until you get focused, use cleanse ghost to reposition and then R.

Apparently there are many ways to play MF.....

General advice:

Get summoner skills that are defensive in nature. Heal, flash, ghost cleanse.
Early game focus on surviving and farming. Kills will come with time.
Last hit only. You pump out too much damage to auto-attack and will make yourself vulnerable pushing a lane.
Stay behind your tanks in team fights. Let them initiate, not you.