This is a four part fugue, so not really a good first fugue. I'd recommend starting with a three voice one.
You should also do several two part inventions, and a few three part ones first. That'll help with the idea of fingering contrapuntal pieces.
To play a fugue such as this, the idea is to have ten fingers, not two sets of five. Voices move between the hands, and need to do so seamlessly.
You should also be aware that you can change fingers on held notes (not playing them again, just moving which finger is holding it down). Those longer held notes also influence which other fingers are convenient to use for the remaining parts.
There are several editions of this on IMSLP, some of them may have some fingering written in - you should check and see what you find to be useful.
You may also find
this analysis useful (scroll down past the Prelude bit if you are only interested in the Fugue).
Step one is to work out fingerings, then practice each voice separately - using the fingers you worked out for the whole thing, then in various combinations of voices. The analysis I linked will show you where the various voices lie and how they work.