Not necessary for you unless you want to force them into producing this year. If you are sure you'll be able to hang on to your garden plot next year, I would suggest just letting them produce for you next spring.

I do want it to produce the first year, as I mentioned above.

I just have no idea how to do it.

The good news is that you never need to worry about losing your artichoke to freezing, but the bad news is you've missed the boat on vernalizing your artichoke outside this year. Vernalizing means you "trick" the plant into perceiving that it's gone through a winter. Many plants won't bloom until they have been through a winter. For artichokes that means some number of days (forget how many off the top of my head) in the low 40s but never as low as freezing. You may be able to do this with your fridge, check some of the other artichoke threads from this year, someone was talking about it. It might be better to plant now and take the loss of this year, though, than keep your artichoke in the pot too long. In the future, if you can start from seed, in your area I'd just start them in the late summer and let them go through a real winter. But go ahead and ask around your area, because I'm telling you all this based on my reading and experiences in my area, which is real different from the Bay area.

I tried to post a follow-up, but I guess it didn't take.

I've done a search here and elsewhere, and all I've found is references to vernalizing (including in the fridge), but no instructions as to how to do it. That's why I started the thread.

I'm hoping someone will give me some directions as to how to do it. Thanks.

Dear Sir, i already read the article concerning vernalizing artichoke seeds a while ago. They mentionned two methods:
1: Seed chilling necessity
2: Plant chilling nrcessity

Concerning seeds, it is a very easy task to put the seeds in the fridge at 2 degrees celcius, or 34 degrees F for 40 days.

Concerning plants, you can put them in a cold mid shaded area from February until March, or put the plants in the freezer at 2 degrees C for a whole month, bringing them outside weekly for few hours to prevent rot.

I myself planted Green globe variety during last year spring, without vernalizing, and they produced during the next February, after having their chilling need.

Hope that helps

In the Phoenix area, I've had good luck planting in the fall. The small artichokes acclimate and are big enough to make it through any light freezes with some mulch. In spring they always provide me with tons of chokes.
I'm now in NC and I have several baby artichokes getting ready to plant out in zone 8. This will be my first time in NC for any gardening at all.