I am making a video similar to this one linked below and they make their text scroll across the screen as it's being read. Any suggestions on how to do that. I am editing on FCPX.

Also, I need to be able to put that twitter icon on the screen as well and am not really sure how to do that. Any ideas would be awesome! Thanks!!

Irish Coaches Read Student-Athlete Tweets - YouTube

Brock,
Check out FX Factory - there are several free titles, including Manifesto text scroll/crawl, which might work for you. The best solution is to use Motion 5 to make your own custom titles, which can include the logo.
For $50 it adds a lot of flexibility to FCPX, and lets you do a lot more for titles, effects generators etc.

I actually do have Motion, but have absolutely no idea how to use it. I guess I will need to find some tutorials

A good place to start is Ripple Training - some excellent courses for Motion, with downloadable project files.
Getting Started in Motion 5 (http://www.rippletraining.com/categories/apple-pro-apps-tutorials/motion-5-tutorials/getting-started-in-motion-5.html)

Give it a try, and you'll be surprised how easy it is to get results like the one you are looking for!