1. Before permutating (rearranging) columns with key, free squares are filed with letter X:

    K   E   Y        K   E   Y
   

   1 F A G 1 F A G 2 V D F 3 F A A 4 F X X

VDFVXDVADXVAAVGAGXAVAVGGGGXAFGGAXGAGVVXFGAVDXGDX

1. Before permutating (rearranging) columns with key, free squares are filed with letter X, for example:

    K   E   Y               K   E   Y
   

   1 F A G 1 F A G 2 V D F <=> 2 V D F 3 F A A 3 F A A 4 F 4 F X X

This means the final encrypted text length will be divisible by key length.
In this example length is 12 and key has 3 letters.
Now we our ciphertext's length is 48
VDFVXDVADXVAAVGAGXAVAVGGGGXAFGGAXGAGVVXFGAVDXGDX
123456789012345678901234567890123456789012345678
It means we have several possible key lengths, as 48 is divisible by:

1, 2,             - Hardly possible
3, 4, 6, 8, 12,   - Possible
16, 24, 48        - Hardly possible

Of which most probably key length is 3, 4, 6, 8, 12.
Maybe now we should find words with this lengths:

JohnsRevenge - 12  
John - 4
Kslkgh ?- 6
ADFGVX - 6
etc

2. Empty boxes are filled with X. It means that last row can have more X-es, because count of X on last row doesn't change even after permutation.

Also probablity of X* pair the least, because usually all unused letters/numbers are in X row (in non-permutated ciphertext).

    A   D   F   G   V   X
    ...
V   B   N   0   1   2   3 
X-> 4   5   6   7   8   9  - symbols in this row are used rarely, so X* is rare 

Back to the game. When trying all possible key lengthes (write cipher VDFVX... upside down, left to right, in 3, 4, 6, 8, 12 columns) the more X-es we have on the last row the more possibility is that we have found the correct key length. (It's about possibility, not 100% correct)

3. Not a fact but interesting:
   @Kslkgh, I think I know the cipher and I think I know the key, but I can't for the life of me figure out what the keyword is...am I on the right track?

@BaileyM Do you mean that you know what the ->keysquare<- is. If you do, you are definately on the right track! – Kslkgh
Seems like he the OP reacted more on keysquare (and doesn't care about permutation key?). So probably key is obvious/easy to find.
Also The key is hidden in a ->method<- I've used on various occasions – Kslkgh again makes me think the key is method name- ADFGVX (also it's length is equal to 6, and 48 is divisible by 6).

TO BE CONTINUED...