If you wish the new database to totally replace the old, just replace the entire folder that you specified when you ran the welcome wizard.
If you wish to add ebooks from one computer to another, you could use the calibredb command-line interface to the calibre database, found in my case in C:\Program Files\Calibre2\calibredb.exe. However, while it can do export, I haven't found any import option.
A funny idea might be to use the calibredb option of restore_database :
Restore this database from the metadata stored in OPF files in each directory of the calibre library. This is useful if your metadata.db file has been corrupted.
WARNING: This command completely regenerates your database. You will lose all saved searches, user categories, plugboards, stored per-book conversion settings, and custom recipes. Restored metadata will only be as accurate as what is found in the OPF files.
This will require manually copying the additional sub-folders of the calibre directory from the source to the target computer (but not metadata.db), then regenerate the database using the restore_database command.