To draw all you really need is a pen or pencil and paper—any kind will work—but you can get richer results on papers that are made especially for drawing and by using pens and pencils that are made for drawing. Drawing supplies are very inexpensive. Here is my basic supply.
It is good to have some kind of little pouch to keep your drawing utensils in. A ziplock bag will do, or any kind of little bag that closes securely. I like permanent felt-tipped pens for drawing. Pitt and Pigma are two good brands. It is nice to have several tip sizes. Pencils with soft leads are nice for drawing. I especially like a nice black pencil like my No. 1 Conte Extra fine drawing pencil. It is the red one near the bottom. Just above it is a short (because it is broken) graphite stick for drawing. I also have Charcoal pencil (medium) and a Conte Sepia Drawing Pencil, which has a nice warm brown lead, but I find it difficult to get a sharp point on it.
I have several erasers. You only need one, but any of these will do. The one in the red plastic case at the top is a draftsman's eraser, as is the "magic rub". The tan one is an artgum eraser. These erasers are better for drawings than either a pink school eraser or the eraser on the end of a pencil, which is likely to leave a mark on your paper or rub a hole clear through it.
My last essential tool is a small pencil sharpener. I like the ones that have two different sized holes for sharpening. They get dull after use. When they do throw them away and get a new one. They are cheap.
For beginners and everyday practice drawing I recommend inexpensive drawing pads over fancy, deluxe paper or beautiful sketchbooks. You don't want to be worrying about "ruining" your sketchbook or conserving it. Paper must not be seen as "precious" or you won't feel free to practice as much as you need to.
I keep my drawing supplies and a variety of sketchbooks in a totebag that I made to sling over my shoulder.