I have tried several ways to embroider on an t-shirt and have found the following way to be the most effective at keeping the t-shirt from stretching during sewing and also to keep embroidery from blending into the fabric too much. The first thing I do is I iron the t-shirt to make sure the area that I will be embroidering on is flat and wrinkle free. Next I flip the t-shirt inside out and apply an iron on cut away interfacing. I use the Inspira brand. I have not seen another brand available. This interfacing makes sure that the t-shirt does not stretch out while it is being hooped or embroidered. It makes a big difference in how well the embroidery looks when finished.
For appliques I take the fabric that I will use to applique onto the t-shirt and I will use a light or medium weight iron on interfacing on the back side of the fabric. Prior to applying the interfacing I iron the fabric to get rid of any wrinkles. A wrinkle in an applique will not make the finished product look neat.
In order to see the center of the shirt well I like to very lightly press a line down the exact center of the t-shirt. This helps me in the hooping process.
Here is the shirt hooped and ready to attach to the machine. Each machine has it's own hoop style. Carefully experiment with yours. One thing to remember is that you do not want your t-shirt to be stretched while it is hooped. The iron on interfacing should help you keep from pulling the fabric too much during the hooping process.
The first stitches that will be sewn of the applique typically are marking stitches. These will show you were to place your prepared applique fabric. Once they are sew carefully place your fabric making sure that the entire placement area is fully covered then. Occasionally I like to tape the fabric in place on the edges but I find that it is typically not necessary. The next stitched that will be sewn are the tack down stitches. These stitches will sew your fabric to your t-shirt with a double stitch. (occasionally I have seen applique patterns that do not have the marking stitches as part of the pattern. Then you will have to know how large the pattern in for placement of your applique fabric for the tack down).
Once the prepared applique fabric is tacked down you will have to remove excess fabric. Most of the time this will require removing your hoop from your machine but DO NOT unhoop the t-shirt. Carefully remove hoop from your machine and using sharp curved scissors clip away excess fabric. Take extra caution not to clip the t-shirt or the stitching. Then place the hoop back on your machine for the final step of the applique.
The last step of the applique will finish off the edges of the applique. Typically a satin stitch is used. It will also add any design to the applique.
If you would like to add on a name or some words to your design be sure to use a Wash n Gone interfacing on TOP of your t-shirt. This keeps the stitches from falling into the t-shirt. Once you have completely finished your design unhoop and cut any jump stitches that remain. Then trim away as much of the Wash n Gone interfacing as possible.
Turn t-shirt inside out and gently pull loose the iron on/cut away interfacing. Trim excess. Clip lose threads. Flip t-shirt again and dab off the remaining Wash n Gone with a damp sponge. Any remaining interfacing will wash away with the first washing. Sometimes I go ahead and rinse the area then toss it in the dryer for a couple of minutes to dry.
I hope you get good results with this method as well! The extra steps are well worth the time, money and effort.
Happy sewing!
The first stitches that will be sewn of the applique typically are marking stitches. These will show you were to place your prepared applique fabric. Once they are sew carefully place your fabric making sure that the entire placement area is fully covered then. Occasionally I like to tape the fabric in place on the edges but I find that it is typically not necessary. The next stitched that will be sewn are the tack down stitches. These stitches will sew your fabric to your t-shirt with a double stitch. (occasionally I have seen applique patterns that do not have the marking stitches as part of the pattern. Then you will have to know how large the pattern in for placement of your applique fabric for the tack down). 
