There are many kinds of cast-ons and one of the more common ones is the knitted cast on or knitting on. This cast on is often quite easy for a beginning knitter to learn because it uses the same steps as the knit stitch. The knitted cast-on is very even and elastic. One thing to beware of is casting on too tightly, this will cause your first row to draw in from the sides and it will create a different tension than the rest of your knitting. One way to avoid this is to use a size of needle larger than the size you will be knitting with to create the body of the item.
First create a slip knot. Then holding the needle with the slip knot on it in your left hand, take your right hand needle and insert it into the loop on the left hand needle from the front to the back as in Figure 1.
Then wrap the yarn around the tip of the right hand needle from back to front as in Figure 2.
Draw the yarn and right hand needle through the loop as in Figure 3.
Then slip the yarn from the right hand needle to the left hand needle as in Figure 4.
The loops on the left hand needle should all be aligned the same way. Try casting on with this cast-on, the cable cast on, and the long tail cast on, until you are comfortable then you can use whichever one you like best or that fits your needs best. I have found that different cast ons lay better with different yarns, some just look better or are more elastic, and work better for me. Although it may not be helpful, once you get to know how to do each of these I think you will know which one you like best. Happy knitting!