How do we know that these planets exist?
Confirming that a planet exists is not as simple as one may think! Here is the 8-step process:
Collect data! Find images taken from telescopes.
Observe said images and create observation charts; for the transit method, observe levels of light; for the radial velocity method, observe for electromagnetic shifts.
Look for extraneous data- Is anything such as an asteroid or debris skewing the data?
Use a second technique, such as radial velocity or transiting, to find the existence of a planet once more- repeat steps one to three.
Use a different telescope to confirm that this data is true
Write and submit a paper detailing the existence is true
Get the paper reviewed by another astronomer
Publish your paper- there is officially a new exoplanet!