The help section on the Microsoft Surface website has the following to say about using the F-keys on the touch/type covers:
"If you want to use a function key (F1-F12), use the Fn key in combination with a key from the top row of Touch Cover. For example for F1, press Fn + Mute."
However if you use a lot of keyboard shortcuts then you'll suddenly discover your productivity takes a dive with the need to hold down yet another key (and for some shortcuts it's downright impossible) .
There is a simple solution however -- pressing Fn + Caps reverses the behavior of the F keys permanently (even surviving a reboot).
Now pressing (for example) F5 will perform a refresh, but pressing Fn+F5 will perform a search.