You're going to need to end or switch threads during your cross stitch project. This method (yes, there are many) is my favorite because it is so simple and it works.
With the thread ending on the back of your design and the thread still in your needle, gently run the needle through one of the stitches you already made; preferably in the same color (so your secret doesn't show on the front).
I like to repeat this at least three more times to make sure the end is secure.
Then snip off the excess very carefully.
Stay tuned for more cross stitch how-to's and tutorials.