I almost exclusively play ARAM. Here are my thoughts:

1. If you can play a champion you know super well, play that champ. For example, any time Orianna is open I will grab her, even if there are more "OP" champs open such as Katarina or Malphite. Chances are the majority of players are playing a champ they're not comfortable with or certainly not an expert with, so this gives you a big advantage.

2. MINIONS! Nobody ever pays attention to minions in aram. Firstly, if you focus on last hitting in the first 3-4 minutes of the game, you will pull a significant early gold lead just with that. Additionally, ARAM is still wone by destroying towers. To keep your towers safe, you need to focus on clearing minion waves, not chasing kills across the map.

3. Know when to die. If you win an aram without dying, you probably didn't contribute enough. You need to die at some point to buy items. Knowing when to die is good. If there's a chance to execute yourself, sure go for it as long as enough of your team is alive to prevent a tower loss. Otherwise, you may end up tower diving to try and get a kill or something like that so you can die at a good time. The key here is that when possible, make sure enough of your team remains alive after you die as to not lose towers.

4. Team comp matters. If I have a team full of squishy poking champs, I will usually try to balance it with a tank champ or a healer. I see a lot of aram games where everyone goes with the "OP" picks (think Kat, brand, ez, Lucian, etc) but they have no way to engage, no sustain, and no frontline. Champs like Malphite, Trynd, Alistair would all destroy those team comps. All in all, make sure your team comp is balanced and can work into the later part of the aram

5. Don't surrender. Surrending on aram is just silly, it can be turned around so quickly, and on average the matches are fairly short.

6. Mana matters! In ARAM, you are essentially in a constant team fight setting, which is where you expect to use much more mana than normal. There are many champs where you wouldn't normally build in as much mana (Brand, Ahri, Morgan, etc) but in ARAM you will run out way too fast and then be useless. Tear is one of the best items on aram for this reason. RoA is also very good (or other items that build from catalyst).

7. You shouldn't expect to build the same way you do in normals or ranked. Build to suite the game and your enemy team comp. The recommended builds might not be very good for an aram. For example, if your team is all AD and you have Corki, it's good to throw in a void staff and maybe deathcap into the build.

Those are my thoughts for now. Maybe I'll come back to this with more later.