Breast size in itself shouldn't usually make a difference. Milk storage capacity varies according to how much glandular tissue you have (which is not the same as how much fat you have), but even if you have a low storage capacity, this can be helped by feeding more frequently.

As mentioned above, making sure the baby is attached well is the main key to success. You need to look at baby, observe how s/he feeds and notice whether your nipples are comfortable, because if you are not average, your good breastfeeding position might not look like examples in books. Some well endowed women find that holding the breast up slightly with a towel rolled underneath, or using a "breast sling", helps keep them in a good position for baby to feed well. If your nipples a very large, it's especially important to make sure baby gets the whole nipple and some surrounding area into his/her mouth.

The main thing to remember is that if it doesn't feel right, or baby doesn't seem to be feeding well and growing, get some help ASAP.