Urgot is a very underused but powerful AD champion that can perform many roles for the team. Early game, Urgot is a monster, capable of zoning out the enemy team with his long range poke. End game, Urgot becomes a tanky, sustained-damage dealer that cannot be ignored. However, not many team compositions are right for Urgot so only pick him if your team has enough damage. Urgot cannot be played as a standard AD range carry because of his short range.

Pros:

Great early game poke/ zone out ad carry
Huge, tanky, late-game threat that cannot be ignored
Decent damage all throughout the game

Cons:

mana hungry early game
short aa range
needs a good team comp to maximize potential

Early game- Urgot is a lane destroyer. Any AD carry will have a difficult time laning against him because of him long range poke. If u can land the noxian charge, they will take 3 acid hunters to the face. Unless you're versing a soraka-vs lane, the AD carry will not be sticking around too long after that harass. Keep last hitting and harass without pushing. Warding is your supports job but always be aware of where the enemy jungle and mid lane champs are. If you know the jungler is at top, you can push the lane to the turret, making the enemy AD miss out some valuable gold.

Mid game- At this point, you should have atleast a brutalizer, merc treads, and a glacial shroud. In team fights, your gonna be the tanky ad carry. You play like a normal ad carry, staying in the back and hitting whoever you can. But if you get an opportunity, swap position with the enemy AD or AP carry and start tanking some damage. Urgot's ultimate gives you tons of resistances, making you very tanky.

Late game- You are the tanky, range AD carry threat. You should be very durable with most of your items completed but the enemy can't afford to ignore you because you have very decent damage. Your focus is to swap with an enemy carry and tank with your team. This is why it is very important to have a good team comp with urgot. You have to judge whether or not your team will have enough damage to compensate for the lack of a true ad carry. However, you ARE a huge threat with the last whisper.

Armor penetration marks provide good damage throughout the game. Added with brutalizer, your opponent will hurt alot after a few auto attacks and acid hunters.

Flat armor yellows mitigate the enemy AD carry's harass. Combined with your passive, you should be able to win trades easily.

Scaling magic resist blues help bring out late game tankiness. It's just a small bonus but cooldown blues work here as well.

Movement speed quints really help make up for Urgot's slow speed. It's great all around.

As the primary damage tool, acid hunter must be maxed first. However, an early point in noxian charge must be taken to start the harass combo. Max the shield second because it adds a long slow to your basic attacks and acid hunter while providing a decent shield to survive mid-game teamfights and trade effectively with enemy champions.

First items are boots of speed and 3 hp pots. Pretty normal. Helps dodge enemy skill shots and provides an extra 450 hp if needed. Take doran's blade instead if you're confident and trading and dodging harass because it will help you with your last hitting.

If you're having a lot of trouble, grab 2 doran's blades. If not, grab the brutalizer. The cooldown and armor pen are really nice. I believe that with the brutalizer, you can hit your target 4 times with acid hunter before noxian charge times out, but I'm not sure :P.

You should try to get glacial shroud as soon as possible. It will help with your mana issues and gives nice armor to counter the enemy AD and cooldown reduction for increased damage output.

Maw of Malmortius gives you AD and magic resist, a good tanky dps item for urgot.

Last Whisper is really the last key item to get. This is what makes you an incredible threat late in the game with no real damage items. Your incredible durable with your ultimate and items but you still rip through enemy champions.

The rest are pretty situational. I usually sell my brutalizer because I feel that I don't need it and that I should get another tank item to fulfill my role better. But, it's your choice if you want to finish upgrading it.

Urgot is a very strong champion with good lane presence. Not many people play Urgot because he doesn't fit in many team comps. However, combined with a good-dps, tanky team (ryze, mundo, etc.), Urgot will shine like no other carry. Overall, Urgot is an underused but poewrful champ that can completely shut down the enemy AD range carry.