It's simple in principle but may be complex in practice. If you open your Thunderbird address book and select the 'tools' menu there is an option to export your contacts data to a file. It offers various file formats: the one that most contacts programs read is 'comma separated' but you may want to experiment with the others also. Hopefully, on your tablet your email program has an option to import contacts data. So in principle you would export the data from Thunderbird to a file, transfer the file to the tablet, and then import the data to the program on your tablet. What can make it complex is the fact that contacts programs don't all store the data in the same way. For example, Thunderbird stores a person's first name and last name in separate data fields, whereas some other programs only have one field for a person's name. If you run into problems like that, you can edit the exported 'comma separated' file in a spreadsheet. Or you can try other file formats as suggested above.

My experience with tablets and phones is that while in some ways they are quite promiscuous, they are not good at this sort of bulk data exchange. The best solution I have found with Android based devices, in particular, is to go with the flow and use the connected Google services. So an Android device can sync to Google Contacts, which stores your data "in the cloud" on a Google server, and then you use an add-on in Thunderbird to sync an address book with that cloud based data. At present, the only addon for this that I know Is gContactSync.

It is not without its difficulties. Google Contacts likes each Contact to have an email address and it makes one up if you don't provide one. Most address books divide an address into elements such as street, town, state/county and Google are a bit different in that they treat an address as a single unformatted string, so switching between these two styles can lead to untidiness.

I don't particularly want my tablet full of phone numbers, nor do I want my phone full of email addresses. So it may be worth running two separate address books, one for the phone and one for a tablet or laptop where email is more useful. Thunderbird provides a useful point where you can see both address books and copy Contacts from one to the other.

I have no knowledge of how Apple users go about this. :-S