How do I remove myself from my moms Apple ID and make my own

If 13 years old or older.

Apple ID - create a new.      

Apple ID – Create         

If under 13 years old, a parent will need to set up Family Sharing to create an ID.

Family Sharing and Apple ID for your child.      

Family Sharing.         

Family Sharing - Set up.        

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. Also set up Family Sharing between the IDs to keep access to your apps/purchases. 

How to switch Apple IDs on your iPhone or iPad.      

What to do after you change your Apple ID or password - Apple Support.   

How to transfer all files from one iCloud account to another.        

Follow the steps in the support document you posted from to create your Apple ID.

Once you are done, sign out of your Mom's Apple ID on your devices in

Settings->Account(top of Settings)->Scroll all the way to the bottom->Sign Out

Settings->Account->Media & Purchases->Apple ID

Settings->Messages->Send & Receive->Apple ID

Settings->Facetime->Caller ID->Apple ID

Then sign back in with the Apple ID you just created.

Once that is all done, you will be detached form your Mother's Apple ID.