I just started playing Mordekaiser, but I felt like I had some things that needed to be said that no one has said in any of the other guides. For one thing no one knows how mord works including your own team so remember that. While he is labeled as a tank he is actually quite squishy if you have low health at the start of an engage because your abilities take health and you'll have a very low shield. You can max your Q or E for damage both do a lot, but Q easily does the most if you can get all three hits off. Don't get rage blade, it doesn't make sense if you think about his kit, slow attack speed and movement speed and his damage comes from abilities not autos so getting 8 stacks shouldn't even happen if you know what you're doing. His w heals, and it does a lot more healing if you have a friend to help ya, so for jungle it's a must. He can be played with basically any items and be successful and in any position, he scales with AD and AP, his shield gets stronger the more health you have so best to get Rylai's or Frozen Mallet earlish. Also you'll want some life steal and attack speed. One attack speed item at most, because remember all it really takes is three autos to crush anyone who's not a full tank. Life steal because you lose health, very fast. I recommend beserker's greaves because early it gives you two stats he really needs, movement speed and attack speed. Lastly masteries (because runes are just whatever you have honestly), Take grasp of the undying because it really helps with getting that health back in fights and the tank masteries are good for survival. I copied these from a bunch of other guides I read, and let me be clear I basically read all of them. Which is why this exists, because no one really knows how to play mord right now and all the guides I see are more like updated season five guides than real explanations of how to build and play the champion.
p.s. if you're looking at this trying to figure out if you want to play Mordekaiser, I'll tell you this: the damage is just not fair, when I said a full Q for a kill I meant it.

You can max Q or E first. E is for farming, and raising your shield up, as it increases it more than your other abilities. Q is for raw damage, and if you get three hits off they'll either be dead or out of lane, likely dead. Farming is hard, so don't over use your E because you'll just end up missing more than kill.

Take the normal ones for your position, but flash is a must - good to get that last auto for the kill or escape. Teleport for top, ignite for Mid, heal for ADC, Exhaust for Support, Smite for Jungle(duh).

I personally recommend Grasp of the Undying because that health stealing can be a big factor in winning the fight. But you can go with Thunderlord's or Death Fire Touch also. Thunderlord's you're looking for those three Q hits and if you fail them then you didn't win anyways. Death Fire's touch for more damage and your ultimate will just murder them worse than it already does. As for the little things inside: you'll want health regen because you use health to power your abilites, 2nd tier doesn't matter, Runic Armor because you'll probably have all of those (and because 45 health is nothing, just like health runes), 3rd tier is up to you I picked more regen but fast summoners could be good for jungle or top, and finally Grasp as I've already explained. Over to ferocity and you'll want more ability damage, more trade damage, more life steal, and bounty hunter because you have no cc.

Starting items wise it really depends on what you're going for in lane. Doran's blade can help get you some more health back and also damage (E and Q scale with AD). Amplifying Tome if you want to annoy the **** out of them with your E, and also start building towards an early item (especially good for getting Will of the Ancients). Doran's shield I haven't tried yet, but it would make poke impossible and also give you health regeneration. Boots if they have long range poke, and also cause you're a fat***.