Companies downsize in different ways. In small companies, where just a few folks are being let go, it could be done one at a time. In larger companies, it will be a big coordinated effort. If your company is in trouble and you get called to a big conference room unexpectedly and don't know what the agenda is, watch out. Not that there is anything you can do about it. Many times this will happen on a Friday, so you'll have the weekend to get over your anger (see below).
Companies are all over the map when it comes to severance packages. You'll be guaranteed unemployment compensation and the ability to continue your medical insurance coverage (COBRA) at a hugely expensive price. Please consider COBRA or private insurance, not just in case you get sick, but also because some insurers (at a new job, for instance) require continuity of insurance coverage to waive waiting periods for existing conditions. This is a complex area. The HR people may be able to give you some advice.
Some companies may pay you a severance 'bonus' based on years of service, but they aren't required to. Other packages I've seen include resume review services or other services to help you find a job. Check these out. If they seem helpful, use them. (It's always a good idea to have someone look at your resume, and see my suggestions at Resume Tips.)
One thing I've noticed is that in companies that get involved in multiple rounds of layoffs, the richest packages tend to be at the beginning, with the last layoffs getting a hearty handshake and not much else as the money runs out. If you are offered a severance package (as opposed to being told you're fired), consider carefully whether the layoff is going to make a difference or whether the company is already in the toilet.
