First, if you have already successfully used your TTDS, you'll need to delete the old kernel from your microSD card (delete TTMENU.DAT, TTMENU.SYS, and the TTMENU folder).
Then unzip the english_v108.zip file on your PC to unpack a file and a folder that are contained in the .zip file. Finally, copy the TTMENU.DAT file and TTMENU folder (apparently there is no longer a TTMENU.SYS file) to the root of your microSD card.
You can then copy any .nds files you wish to your microSD card.
Make sure you use the "Safely remove hardware" utility before removing your microSD card from the reader. Insert the TTDS into your NDS and your microSD card into the TTDS, turn on the NDS, and you should see a list of the .nds files after a few seconds.