Pretty much what P Schnell said, but in different words:
UpKeyDebounce = 0
Do
If UpKey() = 1 AND UpKeyDebounce = 0
Dim Save$(2)
Save$(1) = "Blah1"
Save$(2) = "Blah2"
Save Array "File " + Str$(SaveCount) + ".txt", Save$(1)
UpKeyDebounce = 1
EndIf
If UpKey() = 0
UpKeyDebounce = 0
Endif
Loop
This is called debouncing a key - it will let you press up to do your thing, but will not let you do it again, until you let go of the key and press it again.
P Schnell just forgot to put the bit in about setting it back to 0 when the key wasn't being pressed, is all.
[edit] That's if you want to be able to do it more than once while the program is being run. Otherwise, P Schnell's was perfect for your needs.