Buttkaiser, That's What Enemies Call You

Tanky? Yes, please!

Why would I want to use just tank items, opposed to items like Abyssal Scepter that give ability power as well? To put it Simply, Mordekaiser really doesn't need it. Mordekaiser can put out massive amounts of damage even without AP items. The tankiness he gets with this build will make you so hard to kill, you can destroy WHOLE TEAMS that are in your way.

Runes

The health quints help a lot when laning early game because his shield is substantially weaker than it used to be.
The cooldown runes help a lot with how frequent he can cast his ult on everybody you need to, as capturing a dps champion to use as a pet is quite essential to grab a pentakill all by yourself.
Magic pen instead of AP marks? Why?
Well, again, Mordekaiser simply doesn't NEED AP. He does so much damage without it already that magic pen just seems like a far better choice.

Items

First off, open with a Regrowth Pendant, it's a must because all your spells drain your health, you need something you make up for that. Grab another Regrowth Pendant when you can afford it, and then some Boots of Speed. Work your way towards toward Force of Nature as the health regen is really nice to have, especially once you get tons of health at the end of your build with Warmog's Armor. Now grab some Sorcerer's Shoes and depending on whether they have lots of attack damage grab some Thornmail, otherwise get Sunfire Cape first, as up to this point you don't have very much health. Next off get a Guardian Angel for the sake of resurrection, by this point you should be pretty unstoppable. To close off your build, grab a Warmog's Armor to have an insane amount of health.
If they have a significant amount of magic damage it may be in your best interest to replace Thornmail with an Abyssal Scepter, or even another Force of Nature

Skills, and how to use them.

Max Siphon of Destruction first, this is very important because it's you bread and butter, you get the most shield out of this as well as it being a excellent harassing tool.
Now, at first glance you may wonder why you would want to max your Creeping Death before maxing your Mace of Spades. Well when you use your Creeping Death, you have a constant income of shield until the spell runs out.
One point in Mace of Spades is perfectly fine until you max you Siphon of Destruction, and Creeping Death because I find that it is more effective during team fights more than anything.
And of course taking Children of the Grave at 6, 11, and 15, because it is easily your most powerful skill.

Your main goal in fights and laning is to do as much damage as you can while keeping your shield up as much as possible. When entering any fight, open up with a Siphon of Destruction immediately following with a Creeping Death, then cast a Mace of Spades as you run in to close any distance. Keep on spamming your spells as much as possible to deal mega damage.

Using Children of the Grave correctly is what makes Mordekaiser the beastiest of the beasts.
Using this skill correctly is essential to getting triple-kills, quadra-kills, and even penta-kills. When your laning it is simply finding a champion low enough to cast it on, usually combined with Ignite for max damage, as well as stopping any healing that would destroy your perfect plan.
Team fights are a completely different matter however. When your using Children of the Grave in a teamfight, you must find a dps ranged champion to cast this on, they're usually very squishy so get in there do some damage and cast it combined with an Ignite. If the champion you captured does a lot of damage this is perfect as having them as a pet increases their stats even further. Control your pet using alt + right click and make sure that you target the biggest threats first. This will take them down faster than any other champion EVER.
[Note] It is best to target a ranged dps champion with your Children of the Grave because it's a lot harder to get damage off with a melee champion. The pets are really finicky to control so your best bet is a ranged champion like Ashe, Graves, or somebody else with high auto attack damage.

Summoner Spells

Flash can be interchanged with any other spell of your preference, but Ignite is a must have, considering it pairs up with Children of the Grave so nicely. Some other good spells that you may want to use with Mordekaiser could be Ghost (Good for get aways, and chasing among other things), Exhaust (Nice for slowing down retreating champions, or decimating an opposing champions dps), or Teleport if you want to be able to get around the map quickly to help teammates, defend towers, etc.

Laning

Laning as Mordekaiser is pretty sweet, but it can sometimes be a little tricky to find that sweet balance between harassing enemy champions, farming, and staying alive.

Mordekaiser is meant to be aggressive in lane.
He can be very good at harassing and absorbing any countering ability with his shield. At any chance you can get, hit the enemy champion with a Siphon of Destruction while keeping your distance. It's really helpful if you keep your shield at 50 units or more, to absorb any incoming harass.
When your using your Creeping Death to get the most amount of shield out of it in lane, follow this guide
Purple being your Creeping Death
Green X's being friendly melee minions green +'s being friendly caster minions
Red X's being enemy melee minions red +'s being enemy caster minions
The blue dot is you.

When you use Creeping Death on the second minion in the oncoming wave it assures that you get the most shield by damaging surrounding minions but avoiding the initial minion aggro.

When you're being more aggressive in lane your going to want to use this layout because you get shield from all 6 minions at once, as well as putting you in a good position to harass.

General Tips

Guardian Angel is amazing. Why is Guardian Angel so amazing? Well because while your waiting for it to revive you in the midst of a fight, you are still able to control a ghost that you have captured. I've wiped whole teams just because of this.

Pictures

Summary

Many times I've been able to take out all of the enemy team through just bursting a dps ranged champion then using him to take out his whole team. The tank items make your pretty impossible to kill, and with Mordekaiser's natural damage he can take out all who oppose him.
If you follow this build to a tee, and put in the effort required Mordekaiser should be an unstoppable monster, ranging with a probable 9-20 kills by the end of a game.