How do you get the armor cap on any armor? What perks in what skill trees do I need?
I want heavy armor btw

The AR Cap is 567. Easily reachable with Heavy Armor. You pick the necessary perks in the Heavy Armor tree obviously. You'll know it when you see it.

Smithing will also help you. Just temper your armor on the workbench. You need the necessary perks in Smithing to do better.

If I recall rightly, it's possible to hit the armor cap with all heavy armors except for Iron (and maybe Banded Iron as well), since there's no Smithing perk for Iron armor. Steel might need a good deal of smithing fortification, but I don't know for sure.

There's a glitch you'd need to exploit if you want to make Iron armor hit the cap. It's simple and, if used in moderation, not game-breaking at all.

Good to know.

When at the cap is that an 80%* reduction in incoming damage.

Thinking back that's what it was in Oblivion, yes? I'm guessing/assuming it will be similar here.

*Edited to correct value.

The maximum damage resistance is actually 80%.

Excellent, thank you!

Take a look in http://www.gamesas.com/topic/1342463-complete-character-design-freedom-damage-resist-caps-and-ridiculous-damage-thread-10/ topic.

There's a section in the fourth post on armor values and smithing.

So based off of that, a full suit of well fitted Steel armor, with 1/5 juggernaut will reach 567 AR? Am I reading that right?

Yes, assuming you use alchemy, enchanting and smithing to improve the armor. Read the first few posts on that.

e: Did some testing with smithing only and using improved ebony armor without shield.

With 100 in Smithing (perked up to ebony armor) and 100 in Heavy armor (perked 5/5 in Juggernaut + Well Fitted & Matching Set), you'll hit 524 armor rating, which is close enough to the cap.

This is all confusing to me. It says I need only 3 perks for steel yet it shows 2.. Juggernaught and steel smithing

See my edited post above. Also, I think you overlooked Well Fitted.

The table also assumes that you have the skills mentioned in the first post, that is 100 in enchanting and alchemy with lots of perks invested in them.