Here's what you need at a minimum:
6 matzo sheets
1 (24 ounce) carton ricotta cheese
1 (8 ounce) package shredded mozzarella, asiago, or parmesan cheese, divided
1 (28 ounce) jar marinara (or your favorite jarred or homemade pasta) sauce
Preheat the oven to 350 degrees. Prepare the matzo by soaking the sheets in hot water for about 30 seconds, or until the matzo is pliable but not mushy. Don't oversoak, or else they'll break apart. Then set them on a dish towel and let them rest until they become bendable.
Cover the bottom of a casserole dish with a shallow layer of sauce, then place upon that two matzo sheets (or however many fits neatly in the dish). Layer upon it half the ricotta, mixed with a sprinkling of the shredded cheese. Then put on another layer of sauce. Alternate matzo, filling, and sauce until you get the desired thickness/layers. Your top layer should be matzo covered with a thick sprinkling of shredded cheese. Bake the lasagna in the oven for 30-40 minutes until bubbly and delicious.
Improvisations: The above recipe is super basic (and probably not that delicious). I spiffed it up with my favorite lasagna fillings: ground beef (or meat substitute), four cheeses, fresh herbs, spinach, onions, etc. For a less Italian-American and more Sephardic take on this dish, try the filling combinations from this NPR article on minas, the Middle Eastern version of matzo lasagna.