To make a basic piece of knitting, all you need are two things. First, a pair of knitting needles. Knitting needles come in different thickness, so if you want to make a thicker piece, like a scarf or hat, then you should use thicker needles. If you want to make a thinner piece like a pot holder or finger puppet, then you should use thinner needles. Knitting needles can be made of different materials, such as bamboo, other woods, and metal. I have personally found that bamboo knitting needles are the easiest to work with.
Needles can also come in two ways. There are straight needles, which are the most common. Straight needles can be used to make anything, although if you are trying to make a round piece like a hat, it would be harder to use straight needles. Straight needles look like this:

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The other type of needles that can be used for round projects like hats and finger puppets are circular needles. Rather than having multiple rows when you knit, circular needles have their rows connected, so when you start, you just knit knit knit knit until you want to end. Here is how circular needles look:


And the most important thing you'll need is YARN! Now with yarn, it is a little more fun to pick out. Yearns come in all different thicknesses and colors. For a beginner, a general thin yarn is best. As you get better in knitting a cool yarn to use is called chenille yarn, which is thick and soft.