CORE ITEMS
Always buy Liandry's and Sorcerers boots first two items. I almost ALWAYS go Zhonya's after, however there are some exceptions.
Morello/Demonic Embrace can be bought ahead of Zhonya's if they have heavy healers and need to shut them down, otherwise A L W A Y S go Zhonya's third item.
Liandries -> This item pairs incredibly well with your W and R and the Mythic passive is really good for longer fights in the mid/late game.
Zhonya's -> Zhonya's really speaks for itself I think, you can flash R and Zhonya's to stun a lot of enemies without taking damage.

FULL BUILD
Honestly all of these items are very good on Morgana but they are situational and you can basically combo any of these items, but my main full build is this.
Demonic Embrace -> Great against burning away tanks and prevents them from being healed too much. I go for this Item always if they run a tank support and tank top and also most of the times if they only have one tank, it's just that strong.
Morello -> Very good against multiple sources of healing and against squishies. If they have a soraka always buy this item (unless the tank top is fed, then go for Demonic). Morello or Demonic works great with your W and R to prevent enemies from being healed too much.
Horizon focus -> this item pairs really well with your Q + W combo and helps 'one shot' enemy carries if they get caught by your Q. I build this item mostly as my fourth item but sometimes I'll go for some of the situational items.

SITUATIONAL ITEMS
These items are some of the items you can swap out for Horizon Focus if they suit the game better.
Mejai's -> Yeah. I don't know, I haven't actually bought this that often but if you are really fed and know you will continue to be fed it can work but Mejai's doesn't really have a nice place in the build order for Morgana.
Rylai's -> Gives you some tankieness and obviously the slow is nice with your W or R which means they will be in your W even longer but it's honestly not that good.
Rabadon's -> This item is actually really strong to get as your third item if you are fed, you will just blow up enemies and there isn't much more to say.
Void Staff -> Also pretty self-explanatory, buy this if the enemies are stacking MR.

Now, for the runes, I KNOW what you are going to be thinking. "Shouldn't you go Dark Harvest?" and the answer is: you can. But I am a big big fan of Phase Rush because it allows you to move around after hitting your Q+W combo to dodge any skillshots and later on in teamfights it grants you the ability to quickly move around the fight to position yourself better. On top of this you can Q+W+R and even if they flash away you will be quick enough to keep them in your R range to ensure a stun. I take the other movement speed runes because I feel like it supports this playstyle even further. I take Domination secondary because Cheap Shot and Ravenous Hunter pair incredibly well with your kit. However, if you are really not comfortable with Phase Rush you can go for Dark Harvest, but I have to say I don't feel that much more damage with Dark Harvest.

The pathing is really simple but depends on which side you are on. The only thing that is the same each game is that after buying your starter items, you go to your topside buff and guard it untill 0:50, then you channel your recall and at the last second you ward either your entrance to your jungle or the buff itself. After that you let the recall finish, swap the yellow trinked for the oracle lens and head to your bottom buff. Now let's go from your first camp. Let's start with the most interesting side, which is the red side.

RED SIDE
For the red side you want to do a full clear into scuttle. Start at red and get a leash, go to krugs and smite the big one, afterwards you do raptors, wolfs and then it gets interesting. What you want to do for Blue Buff and Gromp is you want to drag both of them out at the same time to get them close enough together to both be hit by your W, you can then smite the blue buff + your passive will make sure you don't lose too much health. That is your basic full clear for the red side.

BLUE SIDE
This one is way simpler and doesn't involve any cool party tricks. You start at blue with a leash, do gromp and smite it. go to raptors and then red. Now I ask my mid or botlaner to ward the bottom side scuttle in this case because I want to be able to see if the enemy jungler goes for the bottom scuttle, if they do go to krugs after red and smite it, if the enemy jungler doesn't show, I skip krugs and head straight into the scuttle and smite that to ensure the scuttle.

AFTER FIRST SCUTTLE
After you get the first scuttle, you can look to do 3 things. First off, you can look for a gank mid or top, if the waves are in a favourable position and the lane is gankable always go for this, people don't expect how long they are going to be taking damage and most of the time it's a kill. Second, you can look to harass the enemy jungler. Sometimes a jungler comes and contest your scuttle, in this case I spam ping my top and mid because it always leads to a free kill. They want to kill the morg jungle and you hold onto your binding untill your team comes and you can secure the kill, invade his camps and recall. Now if he doesn't contest the scuttle and he doesn't show up on the bottom scuttle you can still go for a quick invade to either scout where he is or take his camps, let your mid and top know tho. Lastly, you can also just run to bottom side scuttle and gank bot or mid if ganking top doesn't make sense or bottom is pushed in really far. If you decide to go to bottom scuttle and the lanes aren't gankable anymore I go to the enemy krugs or gromp and clear those.

After all this you basically gank, invade and clear your own jungle depening on how far ahead you already are. Use smite on cooldown to get blue smite as quick as possible.

I put these two together because ganking isn't really that special.

GANKING
This is really simple, you walk into lane, if they have cc use your blackshield on either you or laner, and Q+W them and keep auto attacking untill the enemy is dead. If they still have flash or dashes, try to hold onto your Q as long as possible.

TEAMFIGHTING
Now teamfighting isn't that special either. You look for picks with your Q (yes even on tanks) and continue to harass them with your Q untill either your team or they engage. A strong move to really turn around a fight if you are almost losing it, is flashing into the enemy backline R+Q+W and Zhonya's. This will stun atleast 1 enemy most of the time and also is a big distraction and gives your team time to either kill the tank or carry.

And that's basically it for Morgana Jungle. She's a really fast clearing and strong ganking jungler capable of shutting enemy laners down by camping them really hard. Most of the times my games don't go any longer than 30 minutes because either you or a teammate is fed enough to win the game.

If you guys are missing anyting or have questions feel free to comment.