Presuming you do well on the first round, most companies bring two or three candidates back for a second round prior to making a final selection, often taking another three to five weeks. We counsel clients to check references directly, once mutual interest has been established, i.e., just prior to an offer being extended. They often ask us to do this on their behalf. Once an offer is extended, a response is customarily expected within a week. Offers are often made contingent upon completing a physical, including drug screen, and verification of credentials, such as degrees, prior employment, and compensation.
Clients expect a candidate to give two weeks' notice to their current employer.
If a relocation is involved, the customary norm is a week between concluding your current employment and starting with the new company. Ideally, the interview process will move quickly, building momentum to the point where an offer is extended and accepted. Unfortunately, sometimes there are unavoidable circumstances that slow the process, despite genuine enthusiasm for the individuals being considered. Sometimes more significant interruptions can delay the process even longer, such as personnel changes or corporate restructuring, etc. Do not read too much into it if you don't hear back immediately after an interview.