In FTP, go to your forum directory on the server. Inside you should see the Skin/ folder. Right click that and go to "change permissions" or "chmod" (it might depend on what client you use, but it should be named something like that).
Another box will pop up, either asking for permissions to use (usually checkboxes) or a numeric value.
In FlashFXP it allows you to set them either way.
If it lets you input a number manually, type 777 and press ok. Otherwise, set it so owner, group, and others all have read, write, and execute permissions. (Check all tickboxes in the main part of the screen in FlashFXP, don't tick anything marked setuid, setgid, or sticky)
This should allow the forum to write to the Skin folder (which it must do in order to install a skin).