Treat this as an upgrade. You won't have a problem with missing columns, because those are in your database. You'll have a problem with missing plugins to access those columns.
- First, of course, back everything up.
- Then install Drupal. It makes
sense to follow @Schnippy's hint and look in the database for the
version number, and install that version of Drupal. Otherwise,
install the current version; it will tell you if it needs to update the database.
- Look in your database (hopefully you have phpMyAdmin available) for tables created by plugins. Use that and your memory to reinstall any modules. You might also look at
admin/reports/updates and see if it'll list your missing plugins.
Later, I recommend installing the Schema plugin, which will report any mismatches between your modules and database tables. This gets reported on the Status Report page and is wonderful when developing a custom module.
If you lost your images and file uploads from your theme or
site/default/files directory, you may be out of luck for that content. Good luck!