Also, follow this steps:
1. Download APK to sd card
2. Use Astro (or similiar) to install
3. Go to settings --> language and keyboard, check swype, exit out
4. Go back to language and keyboard, and go to swype settings, you must complete the tutorial
5. Once done, long press in the google search, and then you will have an option to choose input or swype keyboard, select swype
6. You are good to go.
Also, I don't think you need root to run this.