Lets get right into his pathing, Rammus's jungle pathing can be different but my personal way to get the healthiest clear is by; Unlocking W Defensive Ball Curl and Starting Red Brambleback with a leash, make sure to hit W exactly before it hits you to get maximised damage, After that you unlock E Frenzying Taunt So you can get the attack speed, go to the Krugs and Taunt the big one and make sure to Smite it, After you cleared the Krugs You go to Raptors(you might wanna use one Refillable Potion here) And go into the middle of them and hit the big raptor, like that all of them will be surrounding you and you will get maximized damage on your W, Like that you are level 3 and you have unlocked your Q Powerball. After that you might wanna gank Mid or another lane which is near your red side. After that you do Wolves into Blue Sentinel check Rift Scuttler and Smite it then do Gromp Lastly.

Summary:

Red Brambleback
Krugs - Smite
Raptors - Refillable Potion
Gank - Mid/Top or Bot
Wolves
Blue Sentinel
Rift Scuttler - Smite
Gromp

PROS

- High CC and Peel for your team
- high AoE Magic damage
- Great Gank potential at level 3
- Fast Mobility especially with new Ult
- One of the best tanks against AD

CONS

- Bad at level 2 which makes him easy to invade
- Ability Power (since his kit is based on armor)
- Kiteable
- His Q can be interrupted by a lot of things even minions

Rammus's runes are pretty solid, his primary Keystone is Aftershock it outperforms any other keystone since it provides the extra damage after you hit a Q Powerball, and while they are taunted it will surely hit. Predator might be an option after his new ult, but I don't think its better than Aftershock since you don't need the extra movement speed early on, you usually take predator for jungler's that need a boost when ganking to lanes.

Font of Life vs Demolish, they are both good runes this just depends on your playstyle, do you prefer getting the extra gold on turret plating and helping laners break the turret or you prefer peeling more for your teammates with that little extra healing with Font of Life. I would recommend font of life if you feel like you aren't using demolish consistently.

Unflinching is a good rune since it removes more tenacity which rammus is vulnerable to and also when your W Defensive Ball Curl is active it wont slow you as much. It is better than Overgrowth in almost all situations since you will almost always encounter CC and kite champs.

Next is Sorcery tree with Celerity the reason I prefer Sorcery than Precision especially now, since the new ult Soaring Slam scales with movement speed, Celerity will give you better range to ult and make sure you hit it and get close. Along with Nimbus Cloak which provides the same thing when you flash to get close and make sure to get in range for the Ult.

Precision although is still an option if you prefer so. Legend: Alacrity will give you more attack speed which synergizes with your E Frenzying Taunt which gives attack speed. And with Legend: Tenacity is better against CC enemy comps, since it reduces CC time.

And lastly Triumph which is a good rune when you are the frontline of the team fights and you need to survive till the end since it heals you when you get a takedown, also it helps since it gives the extra gold on a takedown.

Rammus is one of the best tanks against armor, since his kit is based on armor, Make sure you tank for your team and act as the frontliner.

Tips in Ablities

Rammus's E Frenzying Taunt has a passive that gives attack speed, this passive stays active while Rammus has an ongoing ability, this means make sure to W then Taunt so the attacks speed refreshes even on mosnters.

Rammus new ult Soaring Slam is a new mechanic you always need to make sure to have Q active when you use it, there will be situations where you need it for the area damage but mostly you will need it to engage. If you seem that you cant hit your ult, use it after someone engages to make sure to hit it since it is pretty hard to hit.

Early Game

In the early game your main objective is to farm and Gank, when you gank make sure that there aren't many minions in lane, since the enemy can easily stay behind minions and block your Q Powerball. Invades are also an option but remember you might not be able to win fights but you can escape easily with your high mobility.
Make sure as a jungler to focus on the enemy jungle's pathing and make sure to know where he is and get objectives accordingly. GETTING Control Ward IS VERY IMPORTANT!!

Mid Game

In the mid game it might turn into ARAM in the mid lane around this time, if you are the only tank in the team you need to make sure to start engages when its the right time and your team is positioned, start with Q and always ult while your Q Powerball is active, you can engage under tower only with your W since it denies a lot of its damage, but don't dive a whole enemy team under tower you are still in mid-game and you will die. Make sure to focus objectives and don't die when drake is going to spawn, farm to scale up and get tankier.

Late Game

Late Game you are now unkillable and diving is a good option since towers wont hurt you. Making sure to engage at the right time is important getting Elder Dragon is the most objective you should take care of since it is the game changing objective, watch out for Baron and ward objectives. Tank and peel for your team and watch out for assassins like Zed or Kha'Zix that might be flanking your backline, making sure to taunt those assassins and saving your team is important.

Rammus's build is usually full of armor, since like I said before his kit is made to use armor, although you still need to build magic resist against heavy AP comps your only armor will be from Turbo Chemtank and Thornmail if that happens.

Knight's Vow is an item which if you place its active on an ally you will take some damage that the ally you place the item on took. This is good if your support isn't a peeler for your ADC, taking this for your ADC or a Squishy ally is important since they might need the small peel against enemies that can easily kill them.

Randuin's Omen is an item which gives armor and has a really good active, which reduces Crit and movement speed of an enemy near you, this is very good against enemies like Yasuo, Yone, Kindred and any ADC that builds CRIT. This can work with your Q Powerball and then activate it when you are close to them, this is literally like an Exhaust for crit users.

Frozen Heart is really good against enemies that have a lot of attack speed and rely on it like Aphelios and Kog'Maw. It also gives a good amount of armor with its passive tankiness.

Mikael's Blessing is an item which active is a cleanse for allies, you can activate it on allies that are CC'ed to help them escape sticky situations, this is usually an item a Support takes, but it gives Magic Resist so its good against AP comps.

Spirit Visage is an item that gives extra healing and shields, take this if you acquired the Ocean Soul since Spirit Visage can buff the soul's passive and increase the healing which is really powerful, obviously take this if there is AP enemies as well. Also you can take this if there are 3-2 shield casters in your team.