Sorry you're having to do this, I recently had to do it for the first time and followed the instructions on this site, just adding a little every few minutes.
The deed is done. I put 10 or 12 drops of clove oil in 2 cups of water, and added it over a few minutes. I put her in the freezer once she was dead just for good measure. She was my first rescue, and what really sparked my love for Betta fish. Her name was Beth.