I found that bluetooth keyboards worked fine and were my saving grace when I was installing ubuntu on my surface 2, so it may be your specific keyboard that is causing issues. Maybe try a different bluetooth keyboard?
I was using a generically branded Adapt ADK-100 keyboard.
Alternatively, you can try turning on the on screen keyboard. To do this, you'll need to boot into live mode, start the OSK from the accessibility settings, and then launch the install.
If you're using the microsoft surface keyboard, then it's not bluetooth, it uses their special side connector, and needs a kernel patch to get it to work (or did, the last few updates I've done haven't required a manual kernel rebuild, so we may now be ok).
The patch in question:
http://ubuntuforums.org/showthread.php?t=2183946&page=2&p=12844865#post12844865
To build and install this kernel patch, follow these instructions:
https://wiki.ubuntu.com/Kernel/BuildYourOwnKernel
ignore the fakeroot debian/rules editconfigs
line, and at that point instead go and modify the files as per the ubuntu forums code block, then continue with the process.
Best Answer
Video Demo
EDIT: July 11, 2014 @ 6:00PM PST
This has been updated to reflect changes in 14.10 AMD64. (14.04 LTS works fine but 14.10 works awesome out of the box.)
Removed boot repair process. ( This seems to be fine in this release. If you have issues you may want to make sure Grub2 is installed and to run the boot-repair process.)
Added bootloader section, again. (Note: Someone fixed the bootloader issue that was causing customized loaders not to work for GRUB2.)
First
Create a partitioned drive.
Second
Follow the instructions on Geek.com.
Return and follow instructions.
note: I suggest using your SD drive as there seems to be USB compatibility issues in some cases. Also you can simply mount the ISO in Windows and copy the contents to the storage drive, SD or flash.
Third
Prepare partitioned space for install.
Now you can restart.
Fourth
The Intel cpu needs a fan sensor update. I suggest doing this with lm-sensors.
Fifth
Not required but if you have made it this far you want a awesome beautiful device. That ugly boot loader didn't do it for me so I created a boot loader just for the surface.