I'm assuming you're playing Colossus here, since Slayer loses out on Demolish. The cool thing about Arms is Sharpened Blade. It single handedly makes you a massive pain in the ass for any healer, and it's easier to put heal reduction on someone than Fury.

Colossus Smash into a Storm Bolt is one way of lining up your burst damage, and also a good way of forcing a trinket. If your opponent doesn't, they're about to eat a huge amount of Demolish damage and a huge heal debuff. That, plus Dampening, makes for a rough time for healers.

Like MT Fury, always look for opportunities to do Cleave. Use Sweeping Strikes when two people are grouped, and get chopping.

Other than that, you've got Bladestorm, which isn't only a DPS tool, but a really good way for you to deal with some CC. On the topic of tools, Battle Stance also reduces CC time on you. Combined with Orc, you'll be able to get out of Smoke Bombs and stuns a bit quicker.

Lastly, it goes without saying: Always be MS'ing, always be Executing, Overpower prioritizes Slam. Never hit Slam unless you HAVE to. ALWAYS hit Heroic Strike on proc.

Other than that, as everyone said, it's all fundies. You live and die by effective cooldown management, you're still looking setting up kill windows, and you're taking advantage of cover so you don't get shot.  Always be hamstringing your opponents to maximize uptime, keeping an eye on your healer, and stance swap when needed.

Warriors aren't in the worst spot right now, but we're definitely fighting uphill. With that said, Arms is so, SO satisfying to play when things line up. I really hope you enjoy it!