Hey, I play rammus quite a bit. I use him whenver I'm on tilt from getting crushed 3 or 4 games in a row. Time to bring out the tank ! I only have a 53% win rate on him but that's more due to the fact that I get caught in bad habits of going super aggressive and leading the charge into battle when no one is with me ! Ultimately the main goal is to taunt people off the adc or a mage so they can get a kill. But with his ultimate a little AP doesn't hurt.

Bond or stone or Strength of the Ages for your keystone. I don't see a reason to choose any other unless perhaps you wanted to try full AP rammus.

I normally start cinderhulk and ninja tabis. Choosing stalkers blade for slowdown or trackers knife for vision if they are invading my side a lot or just to have vision up to in the tri-bushes if my team isn't doing a good job of warding. After thornmail or zz'rot I assess how I am doing and what I think will benefit me and the team. I might grab rylai's for my ap item which add's 400 health, 100 ap and slow the enemy, when you pop your ult, it's hard for them to get away.

Iceborn guantlet is a good item if they have 2-4 squishes. Give you 20% cdr and 100% damage on next auto after using an ability. Not a good item to try to kill a garen or other tanky champ.

You could also try frozen heart over thornmail for that 20% cdr. Often I will be in battle just doing miniscule damage with my auto praying for that cooldown on my W or Taunt to kick back in. Don't be shy on trying some cooldown items.

Play around with these a bit yourself and see what works. Rammus jg clear isn't the best so I like to add the attack speed to help. Sometimes I'll use my full attack speed runes, sure enough, the jg clear is fast, but a bit less armor/resist so I try to balance it out. You could forgo the gylph of scaling magic resist and add more cooldown, but be sure to buy a magic resist item or magic resist boots to off set !

Max the W first, than the E (taunt) and as always max the ult whenever it pops up.

Rammus is a true tank. He's meant to peel for your teammates. He's pretty strong early though so you can get 5,6,7,8 kills early on the squishy lanes.

Early game with cinderhulk, boots and thornmail/zz'rot is about when he's at his power spike. If their jungler is xin zhao and he want to engaged you in the river, you'll win that battle. Simply curl, taunt, pop ult and powerball him to finish him. Same goes with yi or pretty well any other AD jungler. Ap junglers are a bit harder to lock onto long enough to secure a kill but they'll know not to bother trying to mess with you later.

If your top laner is playing tank such as malphite or nautilus and your support is playing a tanky support such as thresh/braum I would not play rammus jg since your team will have next to no kill power unless your adc and mid are absolute beasts, but don't take that chance, pick a diff jungler or tell your top/support to pick a damage champ.

Too many times i've gangked top lane with our top being malphite into someone like darious or garen and we lock on him use all our abilites only for them to get away with 1/2 health.

Also, before you turret dive, make sure you have the damage behind you ! Don't dive if it's just you and another low damage champ. Make sure you have a mage behind you or competent adc.

Ranked play I'll follow a standard build. Cinderhulk, Ninja tabis or Mercury treads depending on ap or ad damage i'll be facing and whether or not I'll need to turret dive to secure a kill for my team, thornmail generally into either raunduins omen (active is a slow) or spirit visage if their ap's are getting strong and chunking hard. Than add more armor or resist items as game progresses. Just try to secure my adc / top laner / mage some kills and get them snowballing.

Pros :

Tanky
Gap closer (can chase down ezreal, lucian, kalista and kill them)
Great peel for team with taunt

Cons :

Lacks real kill power
Falls off late game
Slowish jungle clear all game

Generally start krugs, smite it, move straight to red, pop my 2 potions from my refillable potion, walk in between the birds, powerball (Q) into curl (W) than smite. Move onto the the scuttle in the river, by that time health should be back up to about 75% with red buff than gank whichever lane is pushed in and secure that first blood. After recall move to other side of jg, clear however you like, generally smiting the gromp for the poison and again gank whichever lane is pushed in. Rinse and repeat till you've netted your team or yourslef some kills and perhaps helps push for a tower.

Rammus jungling is quite easy so keep an eye on the map to see where the enemy jungler is, if he's bot side and your on otherside, move into his top side jg quickly to steal a monster from him, I generally wont' go for two since rammus clear is a little slower.

Just peel and taunt for whichver champ on your team is dealing damage.