Before level 6, you need to play passive and farm everything you can. The only way to take a kill before 6 is waiting for an enemy error (like a Yasuo/Zed all-in) or a good jungle gank. Take care of vision to help your jungle and track the enemy jungle path.

After the nerf of The Dark Seal, I advise to start with Doran Shield's for sustain and facilitate the farm. If the enemy laner is AD, rush Seeker's Armguard. I advise to rush mobility (aproppriate boots + Aether Wisp) against enemies that base their potential in skillshots.

After level 6, you can take down enemies with all-in combo "Flash+3Q+W+E+R+Ignite". When you win the lane pressure, you need to look for steal enemy jungle and take drake. You can gain a lot of advantage if you take the drake before min 14, since you can get several tower plates with drake pet.

Here is your power spike.

When the turrets start to fall, you can start rotations. Mordekaiser shines taking objectives. Focus drakes, unprotected towers and Rift Herald.

You need to keep a good farm if you want to carry. Fight only for objectives, if there is no objective, focus on farm and vision.

Keep focusing objectives with your team and avoid go alone. Remember that you don't have mobility.

In teamfights, you need to stay with your team and focus the enemy who is carrying. Try to get a good enemy pet with your R and manage your shield and health to survive as much as you can. If you have hard melee carry in your team (Kayn, Jax, Riven...), try to heal him with your W. It's important that you never be the initiator.

If you realize that you are the enemy focus, buy Zhonya's Hourglass and Sterak's Gage.