Hi, I'm erik93slash. I main mundo since season 4. Follow this guide get free LP.
(Source: lolskill.net)

Pros:

Nice sustain
Nice chases
Safe farm

Cons:

Weak early
Grevious wound

Teleport: you need it to get back to lane quickly or to gank botlane. You ALWAYS need to check the map after lvl 6, to teleport bot and get fed. It's important to steal kills to your adc with Q. Obviously watch your enemy toplaner to counter-tp him if he ganks bot. If bot is ****ed up, just push and get tower. Don't waste your tp for bronze bot (usually premade boltanes).
Ghost: YOU DON'T NEED FLASH. Ghost it's better, with your ultimate you become unstoppable and you can easy go for enemy's adc. Worth for bronze chases in the jungle. It has a lower cooldown than flash.

Movement speed runes are essential for the bronze chases in the enemy jungle.
Health and mr are a must.
Magic penetration it's worthful for lategame.
You can use armor instead of magic penetration, but it's a sign of weakness

Not much to say here. Just put these one.
Grasp of the Undying is surely better than Bond of Stone. It's worthful for trades on the toplane. You need to get fed, deal damage, you are not a support.

Q: it's essential for your safe farm, chase enemies, steal kills.
W: your BIGGEST damage source. You go in the enemy team with your W and melt them down.
E: just put one stack at level 2 to easy last-hit minions.
R: Nice lane sustain, nice BAITS (use it to get ganked from your jungler), nice CHASES

Must items:
Spirit Visage. It's OP for his passive on mundo. Even if enemy team is full AD, you need to build Spirit Visage.
Sunfire Cape. Just more damage like your W.

Mundo needs tanky items, but don't forget to deal damage.
For this reason, you need to buy the Liandry. Buy it if your team is fed, or simply if YOU are fed. It's the perfect item if enemy team is tanky. It gives you magic penetration, and tons of additional damage for your W and Q spells.

Just farm safe, you are very weak early game. Use your Q and your E to last hit.
If your jungler tries to gank you before lvl6, try to don't give a double kill to your enemy toplaner.
Don't use W too much in early levels cause it costs you tons of health.
Exploit your mastery Grasp of the Undying for gree sustain and easy damage.

When you have bought Sunfire, Visage and Boots, you can go in teamfights and get fed. If you see enemy adc out of position, use ghost + ulti and chase him till the fountain and kill him. You can easy go 1v3 and kill him.
Poke with Q enemy frontline (with Liandry you will deal tons of damage).
Use W in the brawl to melt down every one.
You don't need to peel your adc, you dont have enough cc to do that. Just go on 4 enemies and zone them from the rest of your team. EZ