There are three main styles of breastfeeding covers. The poncho style is a loop of fabric with a smaller hole on one side so you can drape it over your shoulders. Infinity scarf style covers are a large loop of fabric with the same size holes on both ends. A nursing apron is a large square or rectangle of cloth that is attached to you via a strap around your neck, and sometimes your back also. What style of cover you choose will depend on your specific needs. Poncho covers will not slip off your shoulders during feeding, but it may be more difficult to see the baby. Infinity scarves will drape over the same side you are feeding baby on, covering your shoulder. This can be great if the material is a bit stretchy, otherwise baby may be able to flip open the top, exposing you in public.
Nursing aprons usually have some type of stiff material at the top to help it stay open for ventilation and so you can see the baby. They can also be a bit more straightforward when putting on for the first time, you just put the strap over your head with the cloth in the front. All of these types of covers will keep you sufficiently covered, you just need to choose one that fits your style and personal preference.