See, when I first saw this topic, I was scratching my head wondering why this was even an issue, as filling something with color is pretty much automatic. That said though, I realize that's because I've been doing it so long i make assumptions.
Like shekel said, the key is:
Each filed area must be its own complete closed path for it to be filled fully. If you have 2 stripes they must be 2 completely separate objects. Figuring this out isn't always easy if you're not used to the bezier curve/pen tool. The pen tool is probably the single most difficult thing to master using any vector drawing tool, and many people just never figure it out very well unfortunately. It's especially challenging if you are putting points down, and somehow don't join them up.
This: not so much.
The following method isn't necessarily less complicated in some ways, but some of my friends that never cared for the pen tool liked to use this approach:
Usually when I'm doing simple objects is, I start with the box or circle tools. I draw multiple squares and circles to approach the shape of the object, laying them over the top of each other. Once I'm close, I select all of the overlapped objects, and use the pathfinder tool to join them, and then merge. I use a similar method to chop up objects to get close to the right shape that I want using the pathfinder split toolhttps://helpx.adobe.com/illustrator/using/combining-objects.html
Using the box / circle drawing tools is a lot easier to understand (i think) than using any of the line tools. You'll get immediate fills and strokes on your objects.
The last bit of advice I have is: deleting anchor points using the backspace or delete key is destructive to your path. Using the "delete anchor point" pen tool just removes the point and leaves the rest of the line. https://helpx.adobe.com/illustrator/using/editing-paths.html
None of this DIRECTLY answers "how to fill". I'm just trying to address some ways of making it a little more straightforward to work with shapes without having to resort to the harder-to-grasp pen and line functions.