Try not to miss the skillshot too much because it can end up hurting you instead of the enemy since it costs health.
You can use Infected Cleaver to chase down fleeing targets, or you can use it to kite out enemies. It is really versatile.
Because of his toolkit, Dr. Mundo doesn't really need to rely on offensive items as much as almost any other character in the game. He has only one ability that scales with damage items, being Burning Agony and the scaling on it is poor. Building Defensive items instead is a strong choice on him.
If building offensive items feel like a must, Liandry's Torment is a good choice. Building Magic Penetration is also very useful, as it will proc with Infected Cleaver and Burning Agony and is in general, much more useful for him than Ability Power.
Unless the enemy team is full AD, Spirit Visage is a mandatory item for Dr. Mundo. This item increases his sustain significantly. It allows him to heal a lot more from his ultimate and his passive. In addition, it makes nearly impossible to kill Mundo with an AP champion, as very few of them have the tools needed to break through Mundo's massive sustain and tankiness.
Sunfire Cape is one of the best armor items for Mundo, as it synergizes well with Burning Agony, and gives him more damage as Mundo will generally not be building dedicated damage items.
The Dead Man's Plate is a strong choice on Mundo, due to the granted extra mobility that synergises with both Masochism and Sadism. This allows him to become a very strong chaser. The extra crowd control is also fairly useful.
The Zz'Rot Portal is a less used but also viable choice on Dr. Mundo. It can be used to split push and is very strong with a teammate also building this item.
Mundo's biggest strength ingame is his immense sustain granted from his Adrenaline Rush and after level 6, his ultimate Sadism. If correctly played until late game, Mundo can easily become a character that is very hard to kill. Picking character's who can counter his sustain and/or tankiness such as Katarina or Trundle are good choices.
Vayne can be considered a good counter against Mundo. All of his tankiness means nothing against her Silver Bolts. Her sustained damage is too much for Mundo to endure, and because she is an ADC, she can even build sustainherself, and can build an item that can heavily cripple Mundo's sustain. Her mobility also makes it difficult for Mundo to efficiently land Infected Cleavers on her and will often force Mundo to activate Sadism in order to try to escape her. His lack of hard CC gives him another disadvantage in terms of attempting to stop her during teamfights.
Dodge his Infected Cleaver whenever you can in lane, as it can easily melt your health if not watched as well as giving him an opening to attack you.
Grievous Wounds cripple Dr. Mundo heavily as he is heavily reliant on healing himself to function. Mortal Reminder and Morellonomicon are well recommended items to purchase when there is a Mundo on the enemy team. Ignite is highly recommended if you play as a champion with poor sustain against Mundo.