First, pop open a terminal and change into the directory where you have your .bin file. Type ls -l to check if the bin file is executable. You'll see each file preceded by a line that looks something like : rwxrwxrwx. If you don't see the x's, the file isn't executable. To make a file executable, use chmod +x filename.bin and then check to make sure it worked with ls -l. Once the file is executable, you can run it by ./filename.bin and that . at the front is important!.
If all is well, then the .bin file should execute.