The correct way is the same way as a baby. I know, I did it wrong the first time. I sucked my partner's nipples too hard and got blisters in the inside of the lips and gums. The correct way is to take in the area of the breast behind the areola into my mouth. Not just the nipple--it's not like sucking a bottle! Draw the milk out by sweeping the tongue from behind the areola all the way over her nipple against the roof of my mouth. Ymmmmmmmmm. Man, that's great! Repeat for several minutes and switch breasts.
Also at the same time, if possible, draw the milk from the ducts toward her nipple by gently massaging her breasts. Enjoy the power of pleasuring her.
Place your index finger about half way back on your tongue, then seal your lips around your finger. Now suck all of the air out of your mouth and swallow. Notice as you swallow, your tongue presses your finger against the roof of your mouth. It is the combination of vacuum in the mouth and pressure from the tongue that squeezes milk from the nipple, rather than sucking alone.
It depends on the size of the nipple. The way i like is to just get the nipple on the tip of your tounge and suck as you was drinking from an straw, as you suck,press the lips together to get an more suction going on. If she is lacting good, the milk will flow when you start sucking but if not, got to teas the breast to give up it treat, massage the breast, press your mouth on the breast as you suck. Good luck!