1. You need jars. Canning jars. I'm sure there are people out there who reuse pickle and mayo jars from the store, but unless you are canning-for-the-fridge (meaning, making a small batch of jelly and sticking it in the fridge right there and then to use as your current jar of jelly--pickles are often done this way successfully as well), you need canning jars. They are sold by the flat at most grocery stores. They are made by Ball and by Kerr, which may be the same company? Not sure.

2. With the jars you need bands and lids. The lid is the flat thing on top with the rubber seal. The band holds it on. You can reuse bands until they rust. You cannot reuse lids. If lids look damaged or weird (see below), discard. Just don't even go there. The one on the right has some sort of weird spot on it. I discarded.

3. You need something to process the jars in. I use the official canner from Kerr or Ball or whatever. It doesn't have to be that--any large flat-bottomed kettle will work. But the part that is implied here:

4. A few other random supplies that could be substituted for other similar objects:

5. And as Daisy is demonstrating there, you need water. Lots and lots of hot water. Many people, myself included, boil jars before using them. I rest lids in hot water but I don't boil them because I want the rubbery seal to stay hard until I need it to soften and do its job (seal). And hot water to process jars in, too, is key, of course, in "hot water bath" canning. It's such a large kettle of water that I start it on the stove before I do any other prep work (except chopping if I'm working with hot peppers, or pickles which have to rest in cold water a long time first). But straight-forward tomatoes or jam or jelly? The water goes on to boil first.
That's it for the hardware: jars, bands, lids, kettle, rack, a few utensils, pectin (the only "special" ingredient), water, and a stove to heat it on. Towels are good. Spoons. Knives. But those things you probably already have ready to go.
Next up: the basics of jam.