The red berries are fruits that contain two, three or four seeds inside. You need to clean the red berry away and wash and dry the seeds. Then take a pot of seed compost and sow the seeds with about a quarter of an inch of compost on top. I then leave them outside until they germinate which may take a couple of years. After germination they will take another two or three years to reach flowering size.

I've just Googled "Jack in the Pulpit" and had a surprise. In Britain this is the common name of Arum maculatum, or wild arum. In the States it refers to Arisaema triphyllum. Yours looks a lot more interesting than ours! I wrote the stuff below before I found that we may be talking about different plants.

Arum maculatum
Here in the UK they self seed really easily. I don't imagine you'll have a problem getting them to germinate. The generic advice to place just under the surface of damp compost and keep slightly damp should work, I'd have thought.

You may find seedlings popping up where the birds sit and poop. I'll bet they are designed to be spread by birds eating the berries and excreting the seeds.

Arisaema triphyllum
According to Wikipedia, Arisaema triphyllum is pretty poisonous, so handle with care.

This comes from the University of Texas Native Plants Database - http://www.wildflower.org/plants/result.php?id_plant=ARTR

"Propagation
Description: Propagate by root division or seed. Seeds may be sown outside in late fall, 3/4 deep, or the following spring with or without cold treatment. Seeds should not be allowed to dry out. The seeds may not germinate for up to two years. Cormlets can be separated from the parent corm in fall.
Seed Collection: Collect fruits in fall when the berries are red. Approximate collection date for northern U.S.: Late Aug. & Sep.
Seed Treatment: Remove the small brown seed from the pulp. Stratify stored seeds by placing them in moist sphagmun moss and refrigerating 60 days before planting.
Commercially Avail: yes"

For me, Jack in the Pulpit has always been the Arisaema and can be applied to several of the American species.