I haven't the faintest idea what you're talking about! What "other" option do I select"?
And further, what "proper application" do I select to open what type of file?
Are you guys trying to help me or what?
Okay, calm down...of course we're trying to help you.
The vast majority of filetypes have a default application associated with them on your Mac. These should open with no problem. On many of these, you can go to the "Open with" option as you mentioned in one of your previous posts and you'll usually see a list of other programs that can handle that type of file.
For example, Preview might be your default program for opening JPEG files. Simply double clicking on a JPEG will launch Preview and open the file. But if you go to the "Open with" menu, you will likely see other options, such as Photoshop, Safari, etc. In addition, there is the "Other..." option that you mention, in case you want to use yet another program to open the file...a program that OS X doesn't really recognize as being able to open that filetype properly.
The situation you are describing in your original post is one in which you have a filetype that your computer doesn't know what to use in opening it. Because OS X doesn't know what to do with it, there is no default application listed, and there are no alternatives listed. In this case, it will only give you the "Other..." option. This only happens very rarely in my experience, and most often with filetypes I know to not be compatible with any of my applications, but I want to open them in a text editor to get a text string or something out of them for some other use.
So if you know what application you want to use to open this "unknown" file type, you would select the "Other..." option from the "Open with" menu and then select the application. If you don't know what application to use for the file, you need to find out more information about the file and what would be used to open it. We can often help you with that, but we need specifics about what types of files they are.