For the first method of making a centre pull yarn ball I'll show you, you don't need anything but the yarn and your own fingers. This makes it the most convenient of methods. Here's how you start.
First, wind the yarn around several fingers, with the end at the bottom (in this image, you can see the end just under my pinkie). You can do this method either around your first two fingers or around thumb and first finger, whichever you prefer.
Next, start wrapping the yarn around two fingers (or finger and thumb) in a figure 8 pattern.
Keep winding in a figure 8 pattern until you get it good and wide. If you're using a thinner yarn, shoot for 20 or more wraps.
The next part is a bit tricky. Carefully remove the loops from your fingers, wrapping the yarn around the middle a few times in the middle to anchor the loops.
Keep wrapping around the core back and forth until it's fairly well covered. You want to keep those loops from tangling around each other.
Once the core is well covered, keep on going. I like to wrap all in one direction, but as long as the tail end is free, you can change directions and make a round ball, if you like.
As the ball gets bigger, you can change the angle of the wraps slightly as needed so they don't slip out of position and come undone while you work.
When you get near the end of your yarn, do a few last wraps around the middle to hold it all in place.
Then lock the end by tucking the it under in a loop.