The supplies you need to begin are a set of needles, yarn, some paper and a pen (to take any notes you feel necessary).
I suggest worsted weight yarn (gotta love it, so multi-purpose) and one pair of size 7 or 8 needles, 12 inches long, single point. (More about needles below.) With these supplies you can easily learn how to knit, and even make a scarf (with acrylic or wool or specialty yarn) or potholders (cotton yarn).
The fundamentals of knitting are casting on, the knit stitch, the purl stitch, alternating the 2 stitches to create stockinette stitch, and casting off. These are the doorway to more involved stitches and projects. However, your first items are going to be practice swatches, and your first project will most likely be a scarf.
1) Available in 3 styles: single point, double point and circular (more on circular below).
2) Range in thickness\diameter in sizes from 0000 to 50.
3) Range in length in inches as 7, 10, 12 and 14.
4) Available in different materials: Aluminum, plastic, wood, steel, bamboo and old vintage needles can be found in a material called Bakelite and also resin (check Ebay for the last two).
Note: The items you choose to make, and any written pattern you choose to follow, will state what size needles to use and what type\weight yarn. Be mindful in the future of what you'll be making when you do your supply shopping.
If you do any Ebay or garage sale shopping for odd lots of used needles, you may find that while a certain number is stated on the tip, for example purposes #5, it may actually vary from other #5 needles that you have depending on it being American-made or United Kingdom-made. If there is any confusion, however, you can use a needle gauge - a plastic or aluminum card with holes in it through which you poke the needle to check its size. That way, you'll always be certain.
ABOUT CIRCULAR NEEDLES. These are used to work in the round, as are double pointed needles, instead of back and forth on straight needles (although one could use circular needles for back and forth knitting if it is convenient). What makes circular needles different is that they are 2 needles, one at each end, connected by a cord in the middle. Most circular needles currently available as "brand new" have the cord being made out of nylon or plastic. Vintage circulars have the cord being made out of coiled aluminum or coiled steel. When buying circular needles, be mindful of the size of the actual needle (its thickness\diameter) AND the length of the cord.