You want to do damage! You are your teams AP-carry! AD-midlaner in your team? No problem! You deal more damage than those mid-lane mages anyway! This guide is going to explain to you WHY you want to build AP amumu and how to pull it off succesfully! Whatever your teammates tell you, don't let them fool you into going tank. It is solo-queue, so your teammates are worthless. They won't communicate and very possibly feed a lot. YOU want to win, so you have to do it YOURSELF!

You want to flash. You got damage and a HUGE area of effect ult with TONS of damage! Also get the distortion upgrade on your boots if you pull of 1-2 kill flash->ults frequently. Smite-> yeah, you're jungler. You need to be able to secure dragon/barons anyway.

Build the items I suggest and your teammates will call you ''god'' after you rek your enemies solo.
You will do tons of damage, and also be quite ''tanky''. You aren't full-tank amumu, but YOU DON'T WANT TO BE A TANK! You want to carry the sh¡t out of your allies. Still you got 3,5K HP and around 100 armor and MR, cause of the runes. Oh. And you'll have +/- 700 AP.
If you play vs a full AD team and you don't burst them all instantly, you don't build abyssal, but you take an item with armor. Zhonya's (Also has AP, so damage), Randiun (if enemy has many champs with crit items) or Deadman's plate (if they just got AD and you want some more movement to run into the enemy team to rek em) should be your go-to armor items.

Take the masteries I suggest and level up the skills in the order I'm telling you.

The runes I use aren't used by most of the league players. Let me explain why I use them the way I do.

We focus our build on doing damage. We build a lot of Health items, which all also deal extra damage. We do not build any armor in the example build, which would be vs a mix-damage team. So we need some scaling armor and magic resist, to become tanky later in the game. We already got the HP.
We want ability power, because this will speed up clearing the jungle. We build magic pen, because this is huge vs champs.

First off: Don't be triggerhappy with your Q! If you miss it, you miss a huge part of your mobility/utility for 10+ seconds. It's worth to try to walk up to your enemies first.
Also, always make sure your W is on when in battle and make sure it's off when you're outside of battle.

Now some less obvious advice

Start your jungle from the bottom-side and clear the entire jungle. This will give you enough money to go back and shop and start the jungle again from the bottom side.

FARM THE JUNGLE, RUSH LEVEL 6. NO SCUTTLES (they take too much of your time to clear pre-6)

Level 6: If you weren't invaded, you'll still have your flash and you have your ult. Try to gank bottom lane, or any lane if your bot-laners keep pushing. You'll have some AP and mobility boots by now if you bought correctly. Walk up to the bottom lane. DO NOT IMMEDIATELY USE Q OR FLASH. Wait for your opponents to flash/dash/try and escape. After they have done their skills, flash onto them and ULT BOTH. Look at the timer of your ult. When your opponent is about ready to move, Stun that bastard again with your Q.
Note: You might not have to use your flash to stun them both. In this case, don't flash. If the enemy just dash- 'n flashed and you are 95% sure your Q will hit, go for it. But don't flash ult after your Q has been missed. You probably need the 3 sec stun from your ult+Q combined to buy enough time for your allies to have figured out that you ganked and got the enemies even after they flashed.
Good job, you got 1 or 2 kills/assists now.

Oh, try to get all the kills for yourself. You can rely more on yourself than on others.

Mid-game, gank whenever you have ult and try to get in position, before you use your Q. Engage with either Q or R. Personally I'm not the best with skillshots and I like to just start the fights with my R and Q them for the chain-CC. It also shows disrespect, which might lead to your enemy tilting. If you are a god at skillshots, you might wanna start with your Q and IF your ally follows up good enough, you might not have to waste your ulti.

Lategame: Aim for the squishies. You BLOW THEM UP HARD! If they have build banshee's veil, just flash>smite>ult>E>Q those bastards. They'll still die if the banshee passive gets destroyed by your smite.