Hi! MF happens to be my favorite adc and one of my favorite champions, so I'm just gonna leave my input here.
Starting with her abilities, I always max her q first. Always. It's such great poke since the enemy adc usually farms from behind their minions. I'd advise you to not spam it on waves, though. It gets to a pretty low cooldown and you can find yourself running out of mana fast if you continue to spam abilities. I then max out her w for the attack speed boost, and her e last since it's only good for slowing down your enemy or checking bushes. I also take a point in her ultimate whenever possible.
When getting to lane I usually take her q first, though sometimes I take her w if I feel like I'm going to get into a level 1 trade. At level 1, her w can give you a good advantage over a lot of the adcs.
As for items, I usually prioritize attack damage first, armor pen second, and attack speed last.
Usual build (in order):
and then either
or
.
I know some people like to build Stattik Shiv over Phantom Dancer, but I honestly think Phantom Dancer's passive is a lot better for her. It gives her some much needed mobility and works very well with her passive. I also pick The Black Cleaver over Last Whisper because it's passive works really well with her ult and helps out the team a lot more, unless your team is completely made up of AP. I sometimes do pick Last Whisper over The Black Cleaver if I feel like I need to rush armor pen and won't have enough money for TBC, but I honestly think it's a superior item.
Trinity Force is a really good item on MF, but I'd only build it as a last item if I'm absolutely wrecking the enemy team and have the extra gold for it.
When playing MF, it really depends who I'm up against as to how I play. For instance, if I'm against an Ezreal I'm going to play extremely aggressive because I know I'm going to beat him. If I'm against Draven, I'm just going to sit back and farm and try to poke at him. Also, remember that when ulting be very smart about where and when you ult. Before fighting, try not to get hit so you can keep you passive up. Her passive helps by quickly getting you into various positions for a well angled ult. And remember, her ult doesn't always have to do maximum damage to be effective. Many times have I ulted at a specific angle just to separate the enemy team for my team to take picks. Also, having a channel means you should know every bit of cc your enemy has so you can execute your ult with no interruptions.
That's all I have for now, but if I think of anything later I'll definitely add it! (Sorry if it's super long but it's like 6am and I haven't slept and lfadjflajf)