Be sure to make some practice pieces first. There are multiple techniques for doing this; one might work better for you than others.
I think the easiest would probably be to apply fusible to the back of fabric, cut out the letters, fuse them to the fabric, then cover the edges with satin stitch. The thing to be careful about with this technique is that satin stitch has a tendency to create "tunnels" in your background fabric. You usually need to heavily starch the background fabric first (1:1 solution of Sta-Flo liquid laundry starch and water, or equivalent) and/or place a piece of stabilizer under the background fabric. The stabilizer can be tear-away, dissolvable, or even just typing paper (a little more difficult to remove). Also be aware that satin stitching is relatively inflexible. You might want to use a wider stitch that is less close together. If you are good with FMQ, you could do the wider stitch thing free motion. You can also use a decorative stitch free motion. However, most people simply use a regular zigzag stitch with feed dogs up.