I find Mundo to be quite a versatile champion. He can fill the role of off tank, beefy dps, or straight dps. I find the best way to go about utilizing his skills is to build like a tank to start off then throw on some dps items at the end to get yourself some oomph since the other team is ignoring you by now.

Pros:
Nearly indestructible short of 4man focus
High damage potential with few items
Great chaser
Great disruptor
Can zone as well as anyone provided you can land cleaver
CC is a waste to use on him so you are rarely tied down

Cons:
Ignite limits your survivability
Dependent on skill shot early on
Skills cost health, so you can really doom yourself if you don't watch it early game

Red- His auto attack is always deadly thanks to masochism and towards the end it will be what keeps you in fights. His high natural damage and the atk spd items we will get will leave a void on armor pen.

Yellow-Dodge to survive. Pretty self explanatory.

Blue-For cleaver spam. Since I forgo CDR in this build, we need some here.

Quints-Again, we need the armor pen to make him more than a cleaver spam bot.

I just don't get the hype over the 21 pt talents. You have to give up too much from other trees to get there. Most of these are self explanatory, but I will go over the odd ones.

Magic pen-This really helps with the cleaver spam and the burning agony. This is so at least some of their MR is negated so you can stay a threat.

Atk spd-Mundo has high natural dmg, but needs atk spd to utilize it. Every little bit helps and there really is nothing else worth taking.

I prefer exhaust and ignite to help with early kills and to slow down the carries later in the game. Ghost would also be good here as would teleport. You could also take clairvoyance if no one on the team had it, but it shouldn't be a first choice.

Pretty standard sequence. R>Q>W>E. I choose to level burning agony over maso because I go for early health and can stand to farm with it. Plus, with Mundo's slow atk spd early on you can only get a little use out of maso. I get 1 level of e at 4 to help last hit and maybe some early skirmishes.

I start off with regrowth and health pot. This should give you some high lane presence provided you do not fall victim to lots of harass. I try to lane up until 1500ish gold so I can b for my belt and boots. This surge of health should last you in lane long enough to farm up the rest for warmog's and merc treads. Then focus on FoN starting with the negatron cloak.

I focus on tankiness early because the other team's damage is weak and they are focused on upping their own damage. This makes you dominant in early fights.

This is also where I deviate from most Mundo builds. Everyone is high on spirit visage. I find it to be nice when learning Mundo, but it really limits your role in the game to not much more than a nuisance as ignite still kills any healing you can do.

Here I usually go for emblem of valor to help out my ad carry and for my own good. Grab armor next.

I like to finish starks next followed by the crit cloak. Here you have to make a decision. If you are rolling, then build an IE, but if you need just a bit more survivability, go for the atmas. Finish whichever one you didn't go for first.

Alternates:
If your team lacks a true tank, you can swap out phantom for randuin's and possibly atma's for thornmail though without a taunt, it loses effectiveness. You could even slip in a ryails for an aoe slow through bruning agony to help keep them in place.

Mundo is quite capable of a solo lane but I believe that wastes his potential. Having him zone from the bushes and letting that vulnerable carry get creep fed is quite effective. This play style requires a more self less attitude from the player. Mundo can be hurtful with few items for much of the game so it is best to try to let a hard carry farm.

Burning agony and maso can clear creep waves pretty quickly, so pushing is pretty quick.

Don't ever try to kill their tanks up front just because you are tanky. Run right through with burning agony and put a cleaver right into their dps' face. You may not have a true taunt, but a mundo barreling down on that ashe is almost as good as teemo's global taunt.

Use your ult often. It will be up for pretty much every big event so try to stay topped off at all times.