First, have a look at your crochet cast-on with the waste yarn positioned at the top and the last cast-on stitch on the upper right. You should see two yarn ends at that point--one from the waste yarn and the other from where you started with the working yarn.
This is where you will carefully begin to unpick the waste yarn. After you release the first stitch, you will merely need to pull on the waste yarn from the back to "unzip" the remaining stitches. I like to insert my needle into each stitch before pulling out the waste yarn. See below.
Keep merrily going until you get to the last two stitches. Then proceed carefully. Here's why. When you pick up stitches and start to work in the opposite direction, everything WILL BE OFF BY HALF A STITCH. This means that you will need to very carefully pick up what looks like half of a stitch directly to the left of the last most obvious stitch. See?
Be sure to orient it properly from front to back on the needle. It will be a bit tight and "squinchy" (for lack of a better word). Even so, I often work it through the back loop on the first row to make for a tidy selvedge for picking up from down the road. Now, count your stitches to be sure you have the right number. You're good to go!