what steps do I need to take to evict someone in PA. There is no written lease and they do not pay rent.
If your mother agreed verbally to let her neice stay in the unit that may construe a valid contract, even if consideration (money, rent payments) did not change hands.
If your mother wants her out, she should first seek to resolve the issue amicably by asking her neice to vacate the property. She might even consider helping her neice move by paying for her things to be moved to storage or to a new apartment. If her neice does not go for that type of arrangement she should follow landlord-tenant protocol.
She will have to give her neice actual written notice that she wants her to vacate the property. Look online for forms or visit your local stationary. Staples and other places have those forms, or you can visit a real estate attorney.
If she does not vacate within the alloted time your mother can move forward with the eviction process.