Satin stitch is a wonderful option for filling in a space and a great option for beginners, even though I personally avoided satin stitch for as long as possible. I don't know, for me? It looked like it was going to be hard and fiddly to get right - I was a little bit right, a little bit wrong.
I eventually taught myself satin stitch, figured out a few ways to increase my chances of having a nice satiny finish, and now use it in a lot of my work (including patterns for kits!).
I've written out a few steps and tips below, but if you're more of a visual learner (like me!), I've also included a tutorial video below.
Satin stitch is basically the process of making multiple straight stitches right next to each other, resulting in a satiny finish.
Your fabric needs to be tight! I cannot overstate the importance of tight fabric when doing satin stitch, especially if you're using multiple strands of floss.
I always recommend starting from the middle of your shape and working your way out to the edges. This helps you keep your lines as straight and uniform as possible.
If your shape is larger, I also recommend starting by making a few guideline stitches - this essentially breaks your shape down into more manageable and fillable pieces; it will also help keep your lines straight! You can draw these guidelines rather than stitching them; but to be perfectly honest, I can't draw a straight line to save my life - stitching out the guidelines works much better for me. Do whatever works best for you, there are no rules in hand embroidery!
Continue filling in your shape until it's full - if you finish and realize there's a gap here or there, you can always go back and fill in those gaps at the end.
In the video tutorial below, I demonstrate how I fill in a small space with satin stitch, as well as how I fill in larger spaces. Although some would argue that you should use a different stitch to fill in a larger space, I maintain that with proper fabric and floss tension (i.e., TIGHT), you can achieve beautiful results.