My first tip: Make sure you really want to play Mordekaiser. Like, seriously. Why do you want to play this outdated as hell, buggy champion? Do you really want to play him? If you still do, well...
Runes: I suggest basically any tree you feel like, just make sure you have Resolve somewhere in it. You can use something from all of them. PtA, Aery, Fleet Footwork, Phase Rush, Grasp, Glacial Augment, HoB, DH...All of them can work. I've found the most success with Phase Rush, Grasp, and Fleet Footwork, and can definitely see HoB working well, though.
Phase Rush is primarily for chasing (and a bit of engaging) power. Helps a lot for when you actually want to kill someone, and can help when trying to escape. If you're using Aery for poke damage, just follow the same path. Minor runes are Nimbus Cloak, Celerity or Transcendence (probably the latter right now), and Gathering Storm or Scorch (Picked as you desire for the reasons you choose each). I suggest Resolve secondary here, with Conditioning (The extra MR and armor really help) and Overgrowth (As the multiplication will apply to the bonus health you gain from ghosts, making you able to get a lot of health).
Grasp is a beefier, more damaging, more sustaining keystone, but isn't as good for chasing due to the lack of MS gain. Minor runes are: Demolish or Bone Plating (I generally prefer Demolish over Bone Plating on most champions, but it's up to you), and Overgrowth and Conditioning, for the reasons listed above. Precision or Sorcery are your best secondary trees, with either the Tenacity rune and your choice of Triumph, Coup de Grace, and Last Stand, or Nimbus Cloak with Celerity, Transcendence, Gathering Storm, or Scorch.
Fleet Footwork is more sustain and chase, but not as good chasing as Phase Rush. Minor runes are Triumph, Legend:Tenacity, and Last Stand or Coup de Grace, with the usual Resolve runes secondary.
Items are usually copy-paste for me, tbh. Gunblade into Rylai's is a necessity, and usually I want Spirit Visage and Deadman's for their passives and for the defensive power, and I'll usually finish with a Liandry's (Which is a good item on Morde, but there's just so much other stuff you need first anyways). Boots are either the defensive boots or Swifties.
Order is always Gunblade>Boots>Rylai's, then I'll get Spirit Visage or Deadman's as the lead damage type calls for it, then the other, then finish with Liandry's.
Skill Start and Max is usually a bit situational. Start Q or E depending on matchup (Do you need long-range CS before level 2, or are you against Camille? If so, E. If not, Q is fine). Get W or the other one depending on how level 1 went, and how you expect level 2 to go (Will you need sustain, or are they coming past your minion wave to stun you? If so, W. If not, the other one). 3 is always the last ability you don't have. Skill max is usually matchup dependent, as well. First max I tend to default to W for the sustain and decent poke and waveclear, while also being decent DPS, although E is better poke and recharges your shield more than W. Q is only if you think they'll be in melee range for long enough for you to get your 3rd Q off, and you won't need the others for something else.
Second Max I'll usually do Q if I maxed W or E first, or W. By the time I'm maxing this, I usually either have Rylai's or I'm close to having it, so Q is more useful, because I can get it off more often.
Fighting.
1v1 scenarios pre-Rylai's is usually me waiting for them to get close, then using Q and E (and W if they're trying to fight) to deal as much damage as possible. Poking with W and E is also a common thing to do. Usually, if you want to actually kill them, you need your jungler to help, or you need them to hard-engage onto you. Try to keep TP ready to help with drake, since that can mean a nearly-certain botlane turret.
Once you get Rylai's, your chasing potential goes much higher, and you're much more capable of killing someone on your own, as long as they aren't too mobile. Just try to keep the slow on them.
For Teamfights before Rylai's, don't. Legit just don't. Unless you have a Blitz or someone to pull the enemy to you, and your team can keep them locked down, you won't be useful except to stop dives. Just try to get enough gold for that stupid crystal on a stick, and you'll be much more useful.
After Rylai's, it's still mostly waiting for someone else to engage, then you running in and killing them (as they won't be able to kite as well anymore), or you waiting for an assassin to try to dive in, so you can explode them. Put R on your choice of their ADC (so you have a high-damage ghost, as their AS and on-hit items (the only items ADCs will have then, tbh) carry over to a ghost, but the AD (a stat most lack in significant numbers then) is replaced by part of your AD and AP, instead), their tank/juggernaut (for health and a meatshield), or their most-slippery target (Due to it making Rylai's slow constant on them for a while, and so they stop escaping with 100 hp).
Late-game, it's a lot like post-Rylai's, except their tank usually isn't worth ulting unless your team lacks any tank-busting at all. Put it on the ADC to take turrets faster, put it on that asshole that keeps getting away so he stops getting away, or put it on their most fed person (It'll scare them back at the least, and may kill them, giving you shutdown gold at worst, and a crazy-strong ghost at best). Accept that if they have a decent amount of peel, you'll never reach the squishy until you kill everything else.