Opent the site  which you want to use as template....

then got to Site Actions - Site Settings - > Save site as Tempalte

Yes, as long as the base list/site definition exists in the new location
(e.g. some list  templates won't work when you try to deploy in a site
created with a different site  definition), and the WSS/SPS/MOSS versions
match up.

Then how do you get it into another farm to use in that farm?

Once the template  is saved to the template gallery you can download the
file locally, then upload into the template gallery on the new server.

If you are using template  in different site  collection, you need to register the
template using -stsadm command

That depends on where you want to use the template. stsadm is only
needed to create top level sites in a new site  collection, otherwise you
can just add to the template  gallery in each site collection as needed.