Randomly clicking stars or hearing about an exoplanet and then seeing if it is in SE and checking it out. Sometimes I fly ships there and see how long it would take at conventional speeds and FTL speeds.
can I actually go to these discoveries provided they are charted in SE and what is the best way to find them?
Yep you can visit any world that is cataloged and added to the program. You can also add new exoplanets to SE by modifying the catalog files, there are tutorials on how to make custom planets/stars.