You can activate Swype from the Keyboard settings. To do this, go to Settings > Languages and Input > Keyboard Settings. I have a Samsung and as you can see, the Keyboard Swype is available on screen ready to be configured. You need to enable Preditction in order for Swype to work properly. If you have another phone, settings might be different, but you can find them in the same section.
Here is what it looks like: