If you've just installed x-cart, but get a number of MySQL errors when you check the front page, the database may not have been created properly.
To fix this, simply re-run the installation (You will need the auth code from the first installation to do this). On step 3, you have the following option with a checkbox:
Update config.php only
Tick this if you want to skip database importing (it should be empty if you make a full installation)
Be sure that the box is not checked. The language may make you think you're skipping a product import, however, this is the actual setup of the database structure. Product imports can be done after installation.
Continue through the rest of the wizard, and the x-cart site should work now