The situation goes like this: A ex girlfriend of mines came to live with me for a while now she won't leave, She is not on my lease, I am semi aware of something called squatting laws dose this apply to this situation she has been in my apartment for about 2 months.
How do I evict her ?

Did she ever pay rent? Does she get mail there? If the answer is no to both, then she could be considered a trespasser and can just be thrown out. Otherwise she is a subtenant and needs to be evicted like any tenant.

So do I have to go and get a eviction notice then right?
She doesn't pay rent but she has mail that has came to the apartment ?
Like the phone bill but I pay for that?.

Having mail delivered in her name establishes residency, which means you have to go through the eviction process.