This is my coloring process in adobe illustrator. If you made your lineart like in this tutorial or traced it like in this tutorial you can just pick up from there and color your lineart according to these guidelines.
Expanding a traced image
If you traced your image you first need to expand it. Select your entire traced image and press the expand option in the top menu.
Coloring with direct selection tools
Now you have 2 options. Either you select the color areas one by one with the direct selection tool (white arrow) and set the color with the color well tool or select a color in the swatches palette. Sometimes the trace will default to greyscale. You can reset that for individual shapes by selecting a color from the swatches palette.
Coloring with live paint bucket
The other way you can color is the same for both lineart methods. First you need to delete all the white areas in your traced image (if you drew directly in illustrator you can skip this step).
Now select what’s left of your lineart with the selection tool.
Navigate to object/live paint/make.
The lineart must be gap free for this to work. If it’s not you can navigate to object/live paint/gap options. You can mess around with the setting in the newly opened window to fill in the gaps.
Now select the live paint bucket tool. Select a color.
Now if you move the live paint bucket over any surface enclosed by your lineart it will show a red outline of the area you can color.
Click in that area to color it. Do that for every surface of your lineart. Don’t forget the small areas.
When you are finished you need to make the color areas editable. Navigate to object/live paint/expand.
This is basically it. But I usually like to make my colors seem like they are colored in with pencils like in this tutorial.