Federal agencies are notorious for taking a long time to vet candidates for government jobs. The nature of bureaucracy means that the process is a rather long one, and could take up to four or five months.
Federal jobs are posted at USAJobs.gov. Depending on the position, the job could stay open for receiving resumes for up to a month. After that closes, expect another two to three weeks before they begin contacting candidates for interviews.
After an initial interview, you may need to be brought in for second or third round interviews. This process can take anywhere from two to eight weeks, depending on the availability of everyone involved, and the urgency of filling the position.
Once a job offer has been made to a candidate, he may still need to get a security clearance, depending on the level of the job and the agency. Security clearances take, on average, 205 days, according to Clearance Jobs; this is because all references need to be checked out and interviewed, as well as resume details verified. It can help to have a security clearance going into the application process, because that means the agency won't have to pay for it, and you can start sooner.
Of course, time length differs by agency and how eager human resources is to get someone into the position. Each listing is different, so read the notice to see when they want someone. In addition, "freedom to manage" legislation is under consideration (as of 2010), with the intent of making the hiring process faster overall.