Yes, BorrowBox works with eReaders such as Kobo. You need to have installed Adobe Digital Editions first. If you haven't installed this software yet, please visit the Adobe Digital Editions download page and follow the installation instructions provided.
On first launch of Adobe Digital Editions click on Help > Authorize Computer. In the following screen choose Adobe ID from the dropdown menu and enter your Adobe ID and password. If you don't have an Adobe ID yet please click on the Create an Adobe ID link on the right hand side or visit the Adobe login website and click on Get an Adobe ID.
On the download page press the Download eBook button. When you get a pop-up dialogue box asking you whether you would like to Open, Run or Save, make sure that you select Open With and choose Adobe Digital Editions. Adobe Digital Editions will then import the eBook file and you can find it in the Borrowed section on the left side.
To transfer an eBook to an eReader device attach your eReader device to your computer - it should appear in Adobe Digital Editions in the list on the left side. Now just drag the eBook onto the device.