Some hosts allow it, others don't. Ask your host if they allow multiple domains on 1 account. If yes, then usually you will make a subfolder (example: /jim/) and it will act like the root-level of your jim.com domain. So you just install WP in that folder.
If no, then (some hosts) you have to buy another web-hosting account for your second domain. Or switch to a host who allows it.
Now, about the database. You can use a separate database for each blog, of course. OR you can put many blogs in one database, if you just use a different "table prefix" for each (HEY JOETAX, check this out). You set the table prefix in the wp-config file, when you make the new blog. Just change the prefix to something other than the default "wp_" (example, change it to "jim_") and now you can create the second blog with the same database. Very handy if your host only allows you 1 or 5 databases.