1. Go to settings, and select Applications.
2. Check the box to "allow installation of non-Market applications."
3. NOTE: Some of these may be expired. Make sure you check the thread for newer downloads! Download the latest beta version here. If that doesn't work, you can download this older version using the web browser of your choice (NOTE: Dolphin Browser HD seems to have some problems downloading .apks, so try the stock browser before posting about an error), or download it to your PC and transfer it to your SD card. Or can download any of the Nexus One/Droid Incredible custom versions found here.
4. Navigate to the previously downloaded file using a file explorer like EStrong File Explorer or ASTRO click it.
5. Click "Install" to install.
6. Go back to the settings menu and click "Language & Keyboard."
7. Check the box next to Swype. Accept the prompt that pops up.
8. Open up any text field (text message, quick search, address bar, etc), and long press on the field.
9. Select "Input Method" from the pop-up.
10. Select "Swype" from the choices.
11. Start Swyping! Here is a video of the basics:
QUICK SWYPE FAQ:
Q: How do I add a word to the dictionary?
A: Tap the word out like a normal keyboard, then either a) just hit space, or b) press the Swype key.
Q: How do I remove a word from the dictionary?
A: Select and highlight ONLY the word that you wish to remove and press the Swype key. Follow the prompt to remove the word.
Q: How do I easily move the cursor location like the arrows on the HTC keyboard?
A: Drag your finger from the Swype key to the SYM key right next to it to get the interface with arrows to pop up.