What did you type, and what happened/didn't happen?
The .exe file is almost certainly a Windows executable; Linux executables don't usually have .exe on the end of them. You may be able to open/run it using wine, but don't hold your breath.
In which directory is it installed? Let's say it's in /home/user/
1. cd to that directory
2. run the file
Note the quotes: you will need these if you have a space in the filename.
You don't have to be root to install software so long as you install it under your home directory. Most installers will prompt you for a root password if they need one anyway; it's best not to run it as root unless you have to.