When a new president takes office, he has many duties to perform. One of them is to hire new people. A president has thousands of jobs to fill. He will fill some of the most important ones even before he takes office. Afterwards, he will fill many more with the help of the White House Office of Presidential Personnel.
A new president begins to choose his cabinet members soon after his election, if not sooner. He also fills other important posts in the weeks after his election. For instance, when he was elected in 2008, President Obama chose economic advisors early on because of the country's economic crisis.
Other positions in the executive branch will be filled gradually, some by the president himself and some based on recommendations from his personnel office. There are many more positions in the cabinet in addition to the cabinet secretaries. For instance, there are deputy secretaries, undersecretaries, assistant secretaries, and others. There are also more positions in other executive offices.
Important positions, like those in the cabinet, must be approved by the Senate. Others are filled much like any normal job.