Question
For the first time ever I planted a small container veggie garden. My peas are ready to be picked but I'm worried I'm not picking them right. At the base of the pod is the cap where the flower started. Do I pick the pea and leave the cap on the plant or do I pick the pea at the cap?

Answer
Because this is your first time, I will add a few things to my answer, that have nothing to do with your question.
I just like to be helpful.
Because peas are a "cold" crop, they do not like to be hot.
The production will slow way down as the temperature goes up. Because you have yours in a container, you can move them into a cooler, shady area, until the temperature goes down again.
Always remember that peas are seeds. The best time to pick them is not when they are ready to plant, but when they are still tender, and immature. The pods should be swollen, dark green, and crisp. When they have started to turn lighter green, they are too old. Pick these older ones as well, and discard, because if you leave them, it will cut down on your yield. Keep the ripe peas picked every day. This will force the plant to keep producing more peas.

The way to pick them is to take the vine, in one hand,and with the other hand, cut the vine just above the pod, leaving a little bit of the vine attached to the pod.

The reason you hold onto the vine is, to prevent damaging it, or worse, pulling the vine out of the ground. If you can't cut the vine with your finger nails, then use scissors.
If you want to keep the crisp, freshness of your peas, take a bucket of ice water with you when you pick them. Then store them immediately in the refrigerator. Eat as soon as possible for the best flavor.