I wonder how new planets and galaxies can be discovered from earth. I mean, there are not inifinately many directions to look with the telescope, right? Is it really so many different directions to look that there are still directions that noone has ever looked? Please excuse if my explaining is bad, I hope you understand. Thanks.
The principle way of detecting planets and discovering galaxies are completely different.
In general, distant galaxies are faint and their apparent magnitude is high. You need a collect a lot of photons from these objects to obtain an image with desired signal to noise ratio.
The total sky area is in the order of 40000 square degrees. This area has been scanned by a number of survey (viz. SDSS). But all surveys are magnitude limited, meaning they only look for object below a certain apparent magnitude (say 22 Mag).
That is why astronomers build larger and larger telescopes and preferably deploy them on space for better seeing. Newer telescopes allow us to push the magnitude limit to higher numbers and allow us to discover fainter objects.
Exoplanets are mostly detected by indirect methods. More details can be found here https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets. Same as above, advancements in technology will allow us to discover smaller planets which are currently beyond our limits.