Hi, I am the one responsible for FF4kster so hopefully I can answer whatever questions you may have.
The simplest way to start up the program is, as Odbarc suggested, to navigate to the folder you saved it in and simply double click the program (the one just called ff4kster or ff4kster.exe). When the program starts (this could be perhaps more pertinent to your question) you will be presented with a black box with the words "Enter filename: _". I know it's not the most user friendly way to go about it but the program is still a work in progress and at some point I will likely add some kind of file navigation component but for now you just have to type the filename of your rom at that prompt and press Enter. If the rom you want to edit is not in the same folder as FF4kster, you will have to also provide the folder name ahead of it. So for example, if FF4kster was in c:\Program Files\FF4kster but your rom was in c:\SNES\Roms\, then you would have to type "C:\SNES\Roms\ff2.smc" or whatever.
At that point, you should be presented with a blue FF4-looking menu box with the various editors. If something else happens, then something may have gone wrong. Likely causes are typos in the filename and/or path, roms that are not FF2US 1.1, or roms that have been hacked with something other than FF4kster.
Another thing, before using FF4kster, backup your rom. This program is still in beta and as such it could quite possibly cause some problems or otherwise undesirable behaviour with the roms you use it to edit. If something like that does happen, please report it so that I can investigate and hopefully track down the error and fix it, but I would not reccommend using the current version of FF4kster for any major long-term projects.
Also be sure to read the readme! It answers a lot of questions about the less user-friendly aspects of the program (or it should anyway).