Here is the basic idea: You have a bunch of decks of cards (hopefully, you have a student aide to copy, laminate, and cut them for you). Each deck contains 20 equation cards (5 for each conic), 20 information cards, and 20 graph cards. They are corresponding so that students can match each equation to its information and graph. There are also four title cards (with the words Parabola, Circle, Ellipse, and Hyperbola) and eight formula/reference cards (with all the a's, b's, h's, and k's explained).
Each day students learn the characteristics of a new conic. Then they separate, sort, and match the corresponding cards. Each deck is different, so they work with different cards each day. One of my students says to me, "I love this, I wish we could learn all our math with decks of cards".
Each card has a letter, number, or symbol in the corner. There is a key for each deck so you can check for correctness at a glance.
At the end of the investigation (which takes 6-8 days), students can identify conics along with their vertices, opening, center, radius, major/minor axes, and asymptotes. And they can sketch them.
I don't go into any more depth than that at the Algebra 2 level. I think advanced students could do the matching more quickly, and you could follow up with some more in-depth study of all the formulas for the formulas. At our school, I leave that to the Precalc teacher.
I have had some contact with Cindy since NCTM, and recently I asked about her policy for sharing the cards. I have no desire to take credit for Cindy's great idea, I just want to help spread it far and wide so that others can benefit the way my students and I have.
Update August 1, 2014: Cindy's cards are now available on google drive!
Also, I am linking a follow-up post.