Recovery after a total hip replacement depends on many factors. The main factors include your general health, the ease of the operation, blood loss, muscle damage, anaesthetic etc. These all effect the first few days after your surgery. In general patients can be discharged as early as day 2, and may stay in hospital for as long as 7 days. In general 3-4 days is the norm.Depending on the approach used, your early recovery may be different. Most studies agree that all total hip replacements are generally the same after 12 months, however some minimally invasive approaches (like the direct anterior approach) have distinct advantages for the first few weeks to months.
In general, most patients are doing very well by 8-12 weeks.
It is important to discuss your particular situation with your surgeon. If you have had hip arthritis for a long time, or associated knee or back issues, your rehabilitation may be different. All the best.