There's a few ways to extract the texts from Indesign.
You can select all the text and go in "export" and then select RTF as format. You can export as html and then copy that text to a text file if you have texts not linked and in many different text frames. You can create a PDF and export as text but it often cut the sentences and add breaks. You can also export that PDF in html and copy the text, etc.
There's also scripts for this but unfortunately I don't know them.
It's easier to link your text file than exporting the texts; so maybe it will be more work to extract that text first for this time. See below.
To re-import the texts, you can link the text file as you would for an image; whenever that text file will be updated, the text in InDesign will be updated as well. It's also possible to keep some formatting and use the same stylesheet as the one in your InDesign.
But be careful if you make text changes in InDesign, it will not be updated the other way around on the text file! Only do text changes on the original text file.
Your translator will need to be very careful and not add extra page breaks or change too much your own formatting besides the character styles. But this method is still way faster then having to re-insert everything every time; all you'll need to do is relink the text file in InDesign and re-adjust the content because some sentences might take more room in one language and less in another.