The time frames vary by jurisdiction, but here's the most common sequence that must be followed
1) Notice to vacate (in writing using appropriate legal langauge for the state)....normally in three days.
If ignored (which it should be in most cases):
2) Notice of a filing with court for hearing.....normally set within next 7-14 days
If ignored and/or failure to demonstrate cause to NOT vacate
3) Court will order eviction and give five days. At that point, the local constabulary (sheriff etc) can be called on to enforce the order.
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So essentially, it's at least a 15 day and usually closer to a 30 day window wherein proper steps must be taken by the plaintiff (in this case, the current owner).
But regardless of the precise time frame, all notices must be given using appropriate legal documents PRESUMING (sorry for all caps emphasis) that your current occupancy is protected by a written lease agreement.
In the unlikely event you are not under a written lease agreement and are instead living under a verbal agreement, the owner may well be able to have police remove you without any legal evicition steps.