As the title says, I'll talk about laning as Mordekaiser. I don't want to make a long guide, so I'll go right to the point.

Before going to battle, you have to be prepared.

I always get 9/21/0, because of the tank build.

Here is the site with the masteries tree:

http://www.mobafire.com/league-of-legends/mastery-tree-planner#&tree1=0-1-0-3-4-0-0-1-0-0-0-0-0-0&tree2=0-3-0-3-0-4-0-0-3-4-0-3-0-1&tree3=0-0-0-0-0-0-0-0-0-0-0-0-0-0-0

There sure are other masteries, but these ones are my choice.

Best ones:

Exhaust: It's great for any situation. You can exhaust enemies to run away, or you can exhaust an enemy when fighting against him/her. Pretty useful.

Ghost: Same as Exhaust, you can use it to run away or after an enemy.

Ignite: Does a great combo with ult.

Flash: As good as Ghost.

Good ones:

Heal: It can help if you aren't confident about using skills that uses HP.

Teleport: You can get anywhere faster.

Cleanse: If the other team has lots of CC, it'll help a lot.

Fortify: Protect your towers.

Bad ones:

Revive: If I'm going to tell you how not to die, why would you need this spell?

Smite: Jungler Mordekaiser? Not that viable.

Clarity: You don't need mana.

Rally: It's not that useful.

Mordekaiser can deal a good damage even without AP, and here are some tips about his skills:

Mace of Spades: It's not the best option compared to the other skills, but deals a good damage when the enemy is alone.

Creeping Death: Can be used both for offense and defense. Deals a small AoE damage and boosts your armor and magic resistance.

Siphon of Destruction: It's his best skill excluding ult and the first one you have to maximize. Deals a good damage and has AoE.

Children of the Grave: This is his best skill! You can insta-kill an enemy because it deals a % damage when used and then deals overtime damage. If the enemy is killed, he/she will help you for some time. It can be used with Ignite to deal extreme damage and maximize your chances of killing.

Now the interesting part. I think mid lane is the best one for Mordekaiser. He can tank well and deal good damage, so you stay and the enemy will go back.

You have to be careful with champions that can hit you from a certain distance, because they'll only nuke you and, when they have the chance, kill you. It's not that tough though, you can charge your shield and nuke the enemy too. Try to dodge some skills, like Karthus's "Q" or Cait's "Q".

It's the easiest lane, because you have the advantage. Just be careful not to be ganked.

If you want to push, I recommend get lvl 6, kill the enemy, get his soul and push hard. Because if you get ganked, at least you're not alone.

If the enemy team has a jungler, it's another reason to be careful. Junglers usually gank lane that are having problems, and Mordekaiser sure is a champion who causes problem when he's mid.

Maybe you'll find challeging enemies, maybe not.

If you want to kill and push hard, go with a dps or mage champion.
If you are more defensive or the enemies are too hard to kill, go with a support.
If you just want to stay there and protect the tower, go with a tank.
If you want to kill, push hard and kill anyone who tryes to gank you, go with a tanky-dps.

The advantage is that you aren't alone and depending on which champion is with you, things are going to be easy.
The disadvantage is that the enemy isn't alone either, and you don't have the advantage of having a superior defense and offense yourself. And there's the possibility that the enemies are a better combo than you and your ally.

Try to be careful if it's too hard, stay near the tower and ask for help.

Now the situation is complicated. They have total advantage.

Try to nuke the enemies and hug the tower. If you are lucky enough, you'll get a so easy lane that even 1v2, you'll kill them. But that's not the case here.

Try to get any exp point, the faster you get lvl 6, the faster it'll become easier. Be careful not to stay low HP, cause it'll be easy for them to kill you. Why? Your skills use HP, and if you are low HP, you'll not be able to defend yourself.

If you get lvl 6 and get a soul, killing the other one will not be difficult, and you'll have the chance to push. If the jungler helps you too, it'll be even more easier to kill enemies, get their souls and push.

The build is also something that helps a lot.

First, every person has a different way to play and has a build that plays better. I'll teach a common build first.

Start: Doran's Shield or Regrowth Pendant. If you want, you can buy a potion.

Then: That will depend on the enemy team, especially the ones that are against you in the lane you chose. If the enemy lane has mages, get Force of Nature. If they have melee champions, get either Randuin's Omen or Sunfire Aegis.

Boots: Sorcerer's Shoes or Mercury's Treads.

Mid game: Depends on who's dealing more damage: mages or melees? If the answer is "mage", get Banshee's Veil. If the answer is "melee", get the other defense item (if you got Randuin's Omen, get Sunfire Aegis now, or vice versa).

Then: Some AP would help too. I recommend Rylai's Crystal Scepter because of its slow.

Late game: You are supposed to have 3-4 items now. If mages are still a problem, get Abyssal Mask. If melees are the problem, get Thornmail. Both items can be substituted by Guardian Angel. I doubt that you are having problems, but the possibility sure exists.

Then: If you still don't have Guardian Angel, do it. And for the last items, get more AP. If the almost inexistent possibility of having problems is happening to you, try any items of the list below.

Here's a list of useful items:

Defense:

[*] Armor: Randuin's Omen, Sunfire Aegis, Zhonya's Hourglass, Guardian Angel, Thornmail

[*] Magic Resistance: Mercury's Treads, Spirit Visage, Guardian Angel, Banshee's Veil, Quicksilver Sash, Force of Nature, Abyssal Mask

[*] HP: Banshee's Veil, Randuin's Omen, Rylai's Crystal Scepter, Sunfire Aegis, Warmog's Armor

AP: Abyssal Mask, Haunting Guise, Rabadon's Deathcap, Rylai's Crystal Scepter, Void Staff, Zhonya's Hourglass

I created this build, and don't recommend it though. Why? Because you may find it crazy and you have to be an awesome player to use it.

Doran's Shield - Warmog's Armor - Sorcerer's Shoes - Randuin's Omen - Force of Nature - Rylai's Crystal Scepter - sell Doran's Shield and the last item depends on the enemy team

Explaining the build:

First, I don't like to buy potions and wards, I think they are totally useless and waste of money (they aren't, but that's my opinion).

Doran's Shield is a good item to start because gives HP, HP regen and armor.

I try to kill and farm to buy Warmog's Armor. It's good to do it fast because champions aren't strong yet and I'll have HP to use to the rest of the match.

Sorcerer's Shoes gives spell penetration to help killing enemies.

Randuin's Omen gives armor, HP, HP regen, CDR and 20% chance on being hit to slow the attacker's movement and attack speeds by 35% for 3 seconds, that helps a lot when fighting against dps champions.

Force of Nature gives MR, mov speed and HP regen based on your max HP, what helps a lot since I got Warmog's Armor.

Rylai's Crystal Scepter gives AP, HP and slow.

The last item depends on the enemy team, but from the few times I got here, I generally bought Zhonya's Hourglass because of the extra armor and AP. But Thornmail, Abyssal Mask and Haunting Guise are some items I buy too.
Thornmail gives armor and returns 30% of damage taken
Abyssal Mask gives MR, AP and reduces enemies' MR
Haunting Guise gives HP, AP and spell penetration

Tankers: Don't do it. It's too idiot to see two almost invincible champions hitting each other. It's impossible to tell who'll win (it'll take some minutes to find out too).

Tanky dps: I think you'll have more advantage because tanky dps doesn't have so much defense as tanker, and Thornmail and Raduin's Omen] can help too.

Mages: They are nothing. You have MR and damage, they just got damage.

DPS: Easy to kill too. Raduin's Omen can slow attacks and Thornmail helps a lot.

Assassin: They can deal tons of damage. Just be careful, use Exhaust too.

Maybe it isn't the best Mordekaiser ever, but it's already a start. Thank you for reading, and please comment.