One common issue with larger cups in general, and with larger cups on smaller bands especially, is that the strap is positioned way to far out. That causes the fabric to cut into the arm, affects the fit, shape and support of the cup and causes the straps to slip down. If you have narrow shoulders the last one should definitly be familiar too you.
In this tutorial I will be assuming that you are doing this with a sewing machine. This is mainly for simplicity, most people don't know much about making durable elastic seams by hand, and because most people will be using one for this. You don't need anything fancy, just being able to sew zigzag is enough. You also need matching thread and a fresh sewing needle.