With the exception of companies that treat employees so abusively that they just leave in the middle of the afternoon in a torrent of obscenities, for the most part it works as follows:
Employee finds a new job. Employee gives two weeks notice (or more, sometimes). Employer escorts employee off the premises immediately and pays them for two weeks of "vacation".
or...
Employee gets called to a random meeting. On entering, employee sees his manager, one HR person, and possibly one random middle-management "witness" (point #1 - If you ever encounter this situation, immediately demand to have your own witness present, because they legally can and will lie to you about every materially relevant aspect of the ensuing discussion). They hand employee a pile of papers, ask for a bunch of signatures (point #2 - You have no obligation to sign a damned thing, this counts as your last bit of leverage to negotiate for things like prolonged severance, and some of it, such as anticompetes, you do not ever want to sign at an exit interview no matter what they offer you). Employer escorts employee off the premises immediately and pays them for two weeks (or as negotiated) of severance pay.
And yes, for any European friends reading this, that counts as the norm in most of the US. Companies really only deviate from that script in one situation - They so desperately need the employee that the employee actually leaving would temporarily cripple a significant portion of the company. In that case, they play nice and pretend to let you stick around for an extra two weeks - Meanwhile, your computer access drops to the point that you can't do anything but play solitaire (if even that), and you suddenly have a shadow ostensibly there to "facilitate" your knowledge dump (because rookies from security make excellent facilitators, of course).