Multiple users on a single model/assembly

Beware salesmen weilding buzz words.
Only one person can have write access to any document at any one time. So if person A has write access to the assembly, person B has read only access to it. It is possible to change access while you're working, but there are limitations to that, mostly to do with the operating system. The same is true of parts, assemblies and drawings.
SolidWorks has some "collaboration" options which notify you when parts you have open read only have been changed by other users and will allow you to reload the newer versions. You can also request write access.
If you're doing a lot of this you might consider a PDM product.
Matt