As a threshold issue, know that only chametz over the size of a kezayit "counts." A kezayit is approximately the size of an olive. Pesach and chametz is usually most conversion candidates' introduction to a kezayit, but it's an important measurement in kashrut/brachot as well.
So what is this chametz you've got to get rid of?
Chametz is anything made from the following five grains that has also come into contact with water for more than 18 minutes ("fermented"):
So what is matzah? Matzah (matzo) is a hard flatbread that looks like a giant cracker. It is an unleavened bread, and for some people, it's like shellac for your intestines. Some people LOVE matzah and even eat it year-round. Some people spend the week absolutely constipated, so they only eat matzah at the seders, where they are required to. NOTE: Keep in mind that "year-round matzah" usually is not kosher for Pesach. Always check the box.
There are two other issues to consider: kitniyot and gebruchts.
Kitniyot: Kitniyot is allowed to the Sephardi, but not to the Ashkenazi. This is where people get tripped up. To my understanding, kitniyot is a custom that has become a rabbinic prohibition. Kitniyot refers to all the other grains and legumes. There is general agreement that rice, peas, lentils, and beans are kitniyot. Unfortunately, what qualifies as kitniyot can sometimes vary from community to community. Peanuts is a prime example. Potatoes are also considered kitniyot in a few communities. Sephardim generally think that kitniyot is insane. Kitniyot is also given as the prime benefit for an Ashkenazi woman marrying a Sephardi man! (Since wives generally take on the minhagim of their husbands.) A place where I was tripped up is that it appears that you may own and possess kitniyot, but Ashkenazim simply may not eat it during Pesach. As I wrote last week, I was amazed to learn that my pets' food can contain kitniyot.
Gebruchts: This is a Yiddish word for matzah that has come into contact with water. As you might guess, it's an Ashkenazi thing, but it's primarily observed by Chassidic communities. Within the Chassidic communities, I don't know how common it is. It's considered by most to be a stringency, and great rabbonim have ruled that it's not required. The idea is that maybe some part of the matzah wasn't properly mixed with water, and thus, might become leavened. In practice, this means not using matzah meal as an ingredient or as a substitute in recipes. (No matzah ball soup! The horror!) You will see "non-gebrochts" recipes and products in the store. These products normally substitute potato starch for matzo meal. If you're gluten-free, Pesach should be your favorite time of year! Stock up! Better yet, wait until the week after Pesach and buy everything on sale (don't count on the store knowing the exact day Pesach ends. This is no after-Easter candy sale!)