Step 1: RESEARCH: You HAVE to get to know your character. What is influencing you to make them? Cultural influences, celebrities, existing characters, animals, whatever! Put everything that inspires you to make that character into a reference folder so that you can always review it and go back to it when you're stuck on how you want your character to turn out. For example, NiKita is based off of a mix of Alley Sheedy, a little Louise Brooks, and a Borzoi (russian wolfhound). I also looked at existing characters that I thought were close to her body type (or the one I wanted for her) and personality. It's important to look up actors/actresses/celebrities/people that you think could "play your character" so that you can study mannerisms and speech patterns in those people. It will help you make a better, more expressive character. This step is the MOST IMPORTANT. So take your time and really dig around for interesting, inspiring examples that get you excited to create!
Step 2: The Development Process: This is where you take your character and draw them in a bunch of different ways. Mess with their body type (are they fat? skinny? tall? short? ect). Mess with the length of their hair (is it fluffy? wavy? thin? thick? what color is it?), how big their hands and feet are, mess with all of the shapes that you include in your character (head shape, eye shape, body shape, ect). With NiKita, I wasn't quite used to loosening up yet, so I didn't push her as much as I could have. But this is really the part where you want to push yourself to the limit so you can really come out with something creative. Do 12 versions of your character and pick the one you like best :) Also, start thinking about the colors and the shapes that really go with your character (their personality or culture, ect). (Red notes in 3rd image are from my professor).
Step 3: GESTURES! Draw, draw, draw again, and draw some more. This is where you really learn about your character. Draw them in all sorts of poses - twisting and turning and jumping and rolling and flying and whatever else you can think of. This will really help you become comfortable with perspectives, help you loosen up and become a faster, more efficient artist, AND help you become an EXPRESSIVE artist (getting the emotions of your character into the poses is very important!). This stage is where you really dig in and get a sense of how your character would exist in the world you're creating for them. (Green notes in the lower right corner are from my professor).
Step 4: The "Final": I put that in quotes because you'll always want to go back and change SOMETHING. Once you're comfortable with your character, make up a character sheet for them with bio information, color palette info, and anything else you think is relevant. This is a resource not only for whomever is looking at it, but also for you so that you can refer to it and remember the work you've done on your character (who they are). This sheet isn't perfect, but I was QUITE proud of it when I finished it last spring.
So yeah, this is the BASIC process to character design. My experience was more in-depth (15 weeks - including 2 other characters), but it's really something you just have to dive into and see what you can get out of it. It's a super creative process and doesn't come quickly. You're always finding ways to improve, whether that be in general or in a specific step. Just keep looking at others who are doing visual development/character design and see how they work. You'll eventually come along :) practice practice practice!