Welcome to the forum.
Those Effects are easily done by animating the Clips/Titles with Keyframes. Usually, one will at least start by working with the Fixed Effect>Motion>Position, and Keyframing it over time.
While the actual work is easy, one does need to get a handle on the concept of Keyframing Effects. Steve Grisetti, our tireless MOD, has a multi-part Learning Series on Basic Keyframing, available on Muvipix.com. I do nto recall if that particular series is free to all, or is only for subscribers. That will give you a big head-start with the concepts.
There is a similar thread, on exactly what you want to do, and was posted fairly recently. I will look for it, as both Steve and I go into a bit more detail. In the meantime, check out Muvipix.com, and also read the entries on "Keyframing" in the Help File.
Good luck, and will report back with a link to that thread soon.
As Bill said, keyframing is simple and yet a very powerful tool for all kinds of movements of pictures,text,videos,effects,etc. with time.
For moving text, you can also consider text animations. When you apply a text, and the titler opens, then on the right hand side, various text animation options are shown. PrE has got some quite good text animations options available.