Let a friend stay at my apartment. She is not on the lease and was not paying anything to stay. Suppose to stay until she saved money to move. She has been there for about 3 months and I want her to move. She keeps the place nasty and has not paid the cable bill in 3 months as we agreed she would.

First you need to find out the state and city regulations regarding eviction and what is considered a tenant. They vary by state and city. Don't do something without knowledge of the regulations or you could be sued. Typically you give them a 3 day notice to vacate and then file for eviction if they don't move. However, as noted, that varies where you live.

In general if they have been there 3 months, even if not paying rent, you will have to give them notice and if they do not move, formally evict them,

If she agreed to pay the cable bill, that may be enough to constitute an agreement to pay "rent" (to OP as sub-lessor). Thus she is a "tenant", the landlord/ tenant statutes would apply, and OP would need to give her a written notice to quit (with the appropriate time period). If she is still there when the notice period expires, OP needs to take her to court.

On the other hand, if she agreed to pay some portion of the apartment upkeep and has not, that could be considered non payment and entitle to use a Pay or Quit notice to vacate. A Pay or Quit states that the tenant (and she is a tenant at this point) must pay all they owe by a specified deadline or vacate. The deadline will depend on local law.

The disadvantage of a Pay or Quit is that she can pay what she owes and stay. If she refuses to vacate after the notice period expires, they you have to go to court to file for an eviction order.