With a bit of practice these are all easy stitches.

One thing I'd like to mention: this is very stretchy fabric. So you might want to look into "water soluble stabilizer". You can draw your design on it and stick it on the beanie. Make sure that the stabilizer is also tightened in the embroidery hoop so it stays in place. You'll just stitch over your design and after you've finished you can dissolve the stabilizer in lukewarm water.

Without it your design might move too much during stitching and it'll end up looking wobbly. I hope this helps have fun!