"Urgot support? NOOO" says the unbeliever. Then you look at this man(thing, monster? Crab?)'s kit, and go "wait, thats basically exhaust split into three skills, plus a suppression and armor/mr boost for his ult".

Yes, my brothers, Urgot support is basically a walking exhaust. You build yourself tanky and use Q's all game to harass heavily and proc your '15% less dmg' passive. Also, you have no range to speak of except your E-Q combo, so... yea, tanky helps alot. Plus, at full build plus your ult, you are rocking well over 200 mr/armor while still dealing a ****ton of damage.
Also, if the ADC sucks in that game - you can totally pick up the slack.

To explain the gameplay a bit, laning phase you will spend most of your time shooting the enemy ADC in the face. Reason is, A.) Makes it to where he has the hardest time CS'ing, when his attacks do no dmg and B.) your AA and Q's hurt like HELL early game, and he will thusly run away. You will get poked a bit, but as long as you keep that passive proc'ed on him, its unlikely that the enemy bot lane will be able to do much about it unless they have a heal lane or someone like Annie, who can do a little early game damage herself.

FYI: a MASSIVE counter to Urgot bot is a heal lane(IE Soraka) and/or a silence lane(IE Soraka). You ham plays and proc's will be extremely hard to pull off with one of them around.

LVL 2 Advantage - once you hit lvl 2 and get that e, try to see if the enemy ADC is out of position, nuke him if you can, and just go to town on him with you Q's. you can normally get a kill off this if done right, and the other support will have no idea on how to properly save little mcSquish unless they have a ton of heals. During all this, your lane buddy should be happily and peacefully farming while you constantly scare them away with your E's and Q's.
Be warned, you will lose mana fast in this part of the game, make every missile count so going back to base doesn't lose your lane.

LVL 6 and going into midgame. By this time you should nearly have your first core item and a serious power spike with sheen. this is also where you are going to transition into a more tanky role. Basically at this point you are an all-in bruiser. your lvl one ult is super short range, so wait till the enemy tries going after you to get a little vengeance. Go for the squishiest target with your ult - always, and attack the highest dmg target available - always. Mind you, there are exceptions where your suppression is better use elsewhere(like on a fed assassin) rather than on the squishiest target. Patience with your ult pays off, due to how it works. User discretion is advised.
You can start roaming at this point if you have successfully won lane, and you can show your scary *** face to mid lane and start forcing team fights.
also something you can do with urgot early-mid game is tank drag rather efficiently while your adc takes it out, but you need at least lvl 4 to do it.

Late Game.
Here, you are all out tank-support. Yes, you have a bruiser build - use it to scare the squishies and clean up at the end of team fights. Your dueling potential is massive against lower end ADC's and bruisers, and if you can survive the burst, mages as well. Avoid fighting tanks unless you have a LW. You will not do enough damage to eat tanks. Focus your ult on the back line during team fights, and do not be afraid to initiate if you can see an escape after you use your ult to throw a squishy into your front line.
You have ultimate power over people who are out-of-position or think they can face-tank you during a duel. Avoid dueling champs with armor shred(Xin) or copious amounts of mobility(Fizz) unless you think your allies will be there to help you in time.