They don't have extensions because Windows is set not to show the extensions of known file types. This can be changed in tools -> folder view (or something like that), when you're looking at the files.
Anyway, you want to convert the files from .avi or similar to DVD. This will take some time, and there are lots of different pieces of software available.
Do you have the latest Nero with the video converter software? If not, this is free and pretty good:
http://www.erightsoft.net/SUPER.html#Dnload
Use one of those tools to individually convert the files from .avi to DVD format (copy them to your hard drive first), and then convert to a single DVD if this is what you want. Or assemble the avi's individually and then group convert to one DVD.
I'm not sure what the best apps for doing this on Windows are anymore, sadly, It's been a while since I did it on that platform.
Loads and loads of help on this site though:
http://www.videohelp.com/convert#4;10
Lots and lots of help can be found