1. the first question be is the legal to lease your basement in your state, any local ordinances prohibit you from doing that?
2. do you have a signed lease, what is the lease term?
3. did the lease spell out the term on terminating the lease? most state requires 30 or 60 day advanced notice to terminate, including oral lease.
4. yes you are still the owner, so you do have right to evict, you can go file in local small claims or county superior court for non perform.
5. the whole process will take 30-90 days, you will eventually get a eviction order, but depends if the leasehold is legal or not, if it is illegal rental, you may end up refund all rents collected.
6. you can not touch anything in the leasehold till you have procession order, or you be in court for a long long long time, and she will be living there for free for a long long long time.
7. anything she left behind, you must kept in storage for a period of time depends on which state you in.
8. good luck...
haha.