One of the most important steps before starting a project is to read the complete instructions provided. If there is a stitch or a technique called for and you are not familiar with it, practice the stitch in the border of your cloth or canvas.
Before you begin stitching, be aware that your threads may not be colorfast, especially the embroidery threads. Test a red thread or a color that is close to red, since if there is a problem, it will generally show up in this color family. Using a running stitch on a white fabric, put it in warm water for a while and then hang to dry. If it runs, rinse all the threads in a solution of 1/2 white vinegar and 1/2 water. This will set the color.
If you are working on a stamped or counted cross stitch project, and it could take a year or more to complete, you will find that the fabric and generally the white thread are dirty, no matter how hard you keep your hands clean. Use the same recipe of vinegar and water and some Ivory liquid soap and let it dry. If the colors still run, have no fear, just submerge in another solution of water and vinegar and dry. Do this until you are satisfied.