Events Booking support multilingual out of the box, and I am proud to say that it is implemented in a better way than Joomla core. Basically, in Joomla core, for each item (for example, each article), you will have to setup different records, each record for one language
However, in Events Booking you will only have to create one record, then translate to different languages in Translation tab in add/edit record screen.
To setup Events Booking on a multilgual website, you will need to do the translation on a different places below:
To that, go to Events Booking => Translation, translate the language items used in the extension to all languages used on your site
On Categoires Management screen, click on a category to edit. Look at Translation tab, translate the category to all other languages (beside default language) used on your site
On Events Management screen, click on an event to edit. Look at Translation tab, translate the event to all other languages (beside default language) used on your site.
On Locations Management screen, click on a location to edit. Look at Translation tab, translate the location to all other languages (beside default language) used on your site.
On Custom Fields Management screen, click on a custom field to edit. Look at Translation tab, translate the custom field to all other languages (beside default language) used on your site.
The final part you have to translate is Emails & Messages. Access to Events Booking => Emails & Messages, look at Translation tab, translate all the messages to all other languages (beside default language) used on your site.
Sometime, you might see an SQL error when your site is a multilingual website because the database tables lack some require fields to support multilingual. If that's the case, please access to Tools => Fix Database Schema. After that, the error should be gone.