You've cut your thread, separated the strands, and threaded the needle. Now what? How do you make first stitch(es) and secure the thread?? There are several ways do it it.
The two most common ways are the anchor method and loop method.
Anchoring or Weaving
Anchoring happens at the beginning. Weaving occurs at the end. When making your first stitch, pull the needle up through the fabric and leave about 1/2 inch of thread on the backside of the fabric. As you create your first few stitches, the thread (or "tail") is covered so that the floss is secured in place. It takes a little time to make sure you 'catch' the tail on the backside, but well worth it! Weaving is essentially the same thing only in reverse. When you're finished with a color or line of stitches, you slide your threaded needle under 4-5 stitches on the backside of the fabric. Then trim the floss close to the fabric.
Starting out, you can secure your thread via the loop method. Take one strand of thread floss, fold it in half. Thread the two free ends through the eye of the needle (You should have a loop dangling). Bring the needle/thread up from back of the fabric to the front, leaving the loop dangling in back. Form the first half of the cross stitch by putting the needle trhough from front to back. As you pull it through, slip the needle into the loop on the backside. Viola! The thread is secured. (Note: You shouldn't use this method when using varigated threads, if you want to get the full effect of variation.)
I don't really know any stitchers who do this, but this might be easier some who've had problems with anchoring. Thread the needle and knot one end of the floss. Push the needle down from the front of the fabric a short distance away from the area you want to start stitching. Then start stitching, covering the thread with the first few stitches. When the thread is securely covered the knot can be snipped from the end.