How can I deal with Enemy Armor?

Difference between BF4 and BF1 armor

Unlike in BF4, where only AT weapons dealt any damage to tanks, in BF1 most weapons deal some (albeit little) damage. Regular frag grenades, incendiary grenades etc. In fact the recent Fall Patch has increased the damage regular grenades deal to tanks.

Another thing is that unlike in BF4 where rear-armor was a tank's weak spot, in BF1 it's the tracks. Tanks can be easily immobilized if attacked from side.

AT weapons

All classes can equip light AT-grenades, which deal much less damage than heavy AT-grenades, but are lighter, and thus easier to throw farther.

Once you level up your assault, you'll gain access to AT mines, as well as the AT "rocket gun".

Snipers have K-bullets, which are specifically designed to damage armor.

Anti-tank rifles spawn as a battle-pickup (for example there is one at E flag on Sinai Desert Conquest).

Field guns and fortress guns also do high damage to armor and can be operated by any class. Their downside is that they're stationary.

HE mortar can do significant damage to tanks without the need of exposing oneself to direct fire.

AT mines, which can be dropped either by Assault or Artillery Trucks are extremely effective - 3 mines can currently take out any armor in the game.

And of course, tanks are vulnerable to bombs dropped from airplanes. The Attack Plane can be equipped specifically for tank hunting.

I'm late to the party, but just to answer more specifically, every class has its own gadgets that will damage armored vehicles over the usual grenades that every class can equip (they all do some damage besides smoke grenades) and some of the meelee weapons (there's a specific icon when you go to the Customize section and pick a meelee weapon to see if they damage armor or not). As previously mentionned you have all of the stationary weapons to take into account since they will usually do a lot of damage to balance their downside, and the elite class, but if we go class by class and look at all the gadgets:

Assault

By far the best class to quickly kill heavy armor. Anti tank grenades will do a lot of damage, and depending on what else you equip, you will usually be able to deal with ennemy heavy armor all by yourself. I personally like the AT rockets to add some range (also really useful against some of the Behemoths) but the AT mines are obviously the strongest (although being slightly less versatile). Dynamite (C4) must also be mentionned here.

Medic

Although not the worst class against armor, it's probably the one you will see the least used because people will usually use the syringe with health pouches/crates. To damage heavy armor more than with the grenades, you will have to rely on the rifle grenades gadget. They won't do ton of damage but you can easily get some damage while being hidden and it can be used from far enough that you shouldn't worry about being blown off by the tanker.

Support

My favorite gadget right now is the Limpet, and that thing will do a ton of damage to a heavy tank. Depending on where you put it, you can disable most vehicles with 1 or 2 Limpets. And being Support means you can resupply yourself quickly enough to drop a second one provided you have some basic cover. Limpets are also good to destroy buildings or to throw down a ladder. Alternatively, mortar (especially the HE version) will do decent damage to armored vehicles while you're not exposing yourself to direct fire. It's also good against infantry (mortar airburst might be prefered in that case however).

Scout

Definitely the weakest class against armors, you don't want to be close to a heavy tank. However, you will see more K bullets on the average battlefield than medics with the rifle grenades, just because you don't have as many must-include gadgets in the scout class. K bullets act as 5 extra bullets for any scout and will do 5 damage to heavy tanks (or more to other vehicles). They can also rip apart planes pretty quickly. They can be shot from extremely far and will prevent tanks trying to repair. Very useful gadget in my opinion and even though you won't get a lot of kills with it, it will help your squadmates or teammates finishing off a tank.

The first hours I played BF1, I was definitely lost and thought armors were too powerful. Now, I know it takes less than 3 seconds for any heavy armor to go down if a whole squad gets at it. I think it's pretty well balanced, the best tankers will still manage to get good scores and sometimes not die once in a Conquest agaisnt unorganized teams but as soon as you have one good squad playing to win in a team, they should take care of it if it's too good and taking care of important chocking points or flags.