It is easier than you think, if you have never sewn a button on. Here is a simple chart that I found. We used to learn to sew in school many moons ago. When my kids were little I took some loosely woven fabric (like burlap) a large embroidery needle that was rather blunt on the end, large buttons and showed them how to stitch the button on. It was great for small motor skills. I am one of those women that find handwork relaxing and sew when I am watching tv. I always add a drop of clear nail polish to the thread when I am done. But, be careful not to drip on the shirt.
When you purchase a button down style shirt from a store... seal the thread on the button right away. Tame that stray thread that gets pulled and the button falls off before you have to break the thread out and find a matching button because the original button is lost.