Food manufacturers have responded to Passover by creating new and innovative Passover prepared foods. Need to know if something is kosher for Passover, just look for the "P" on the label
Generally speaking, the first rule of thumb of Passover in America, is to look for a "P" on any labeled product as well as the designation "Kosher for Passover." But a label saying it is OK for Passover, without an endorsement, is not always good enough. Familiarizing oneself with the well-known rabbinic, kashrut supervising authorities is also a good idea. The largest and most widely respected kashrut supervisory agency is the Kashrut Division of the Union of Orthodox Jewish Congregations of America (OU). They are the owners of the registered service mark, "P."
Then of course, who you are, also determines what you eat on Passover. Traditionally, Ashkenazi Jews, (Jews of Eastern European descent) do not eat legumes (kitniyot)—beans, corn, peas, rice, etc.—or products containing them as ingredients throughout Passover. Sephardic (Jews of Iberian descent), Yemenite and Mizrahi Jews do eat kitniyot, but they often have varying customs from one community to another as to which legumes are permitted for Passover.
Just to clarify, though, these leguminous vegetables or kitniyot are NOT chametz and, unlike the 5 forbidden grains (wheat, barley, oats, rye and spelt), you can possess kitniyot on Passover and use kitniyot for things other than eating like pet food, cornstarch baby powder, etc. Ingredients derived from kitniyot like corn oil present another layer, with some rabbis permitting their use and others not.
Then there is quinoa. Some rabbinical authorities disagree as to whether or not quinoa, the seeds of the goosefoot plant, should be considered kitniyot. Some pro-quinoa rabbis feel it is acceptable because quinoa was not on the Jewish radar when it was decided to ban kitniyot for Ashkenazi Jews. On the anti-quinoa side, some rabbis disagree and say that it should be banned, because it looks a bit like other forms of kitniyot. The Orthodox Union (OU) recommends that even if you follow the pro-quinoa option, sift through the quinoa before using it to check for any errant chametz grains.
While many observant Jews use matzoh meal and other matzoh related products, there are other Jews who add additional restrictions to their Passover diet. Some avoid any food stuffs made of gebrokts (matzoh mixed with water) products out of concern that the mixing of matzoh and water could lead to any form of fermentation or rising, therefore nullifying the kashrut of that Passover item.
Because of the large number of food products which contain chametz, kitniyot, or their derivatives, don't forget to check your labels for the proper Passover certification and rabbinical supervision. But some products purchased and unopened before the start of the holiday, like milk and regular coffee (as long as they have an OU on them) are acceptable. It's a very complicated world when it comes to Passover, so when in doubt over any foods or medicines not carrying rabbinical supervision, check with your local rabbi.