In general, the best method for putting lettering or designs onto fabric is embroidery or silk-screening. But embroidery requires either a great deal of skill, or some expensive equipment. There exist some silk-screenable fabric dyes, but much lettering is done with regular screening inks onto the fabric. You can tell the difference by handling T-shirts and sweatshirts, and feeling for whether the lettering makes the fabric stiffer. But silk-screening is way too much hassle for just one or two items. So here's what I did for Mac (hearing dog):

I bought a couple of orange mesh vests from RC Steele @ $3.50. They're no longer in their catalog, but they MIGHT still have some.

For reasons that will be obvious in a minute, I wanted simple block letters, with no serifs, etc. So I used Windows Write (Mac users can substitute similar programs) to create a Landscape Mode page with "HEARING DOG" in about 100 point Helvetica Bold. I then used a laser printer (HP LJIIP) to print it out onto a sheet of thin cardboard (cut out of a UPS overnight envelope). You could also print onto paper and xerox it onto cardboard with a Canon or similar personal copier. For these and similar projects, it is well worth your while to figure out how to set your printer for its straightest paper path, and find out what are the heaviest materials that it can handle.

Then I cut out the letters using a swivel knife. An Exacto knife with a fresh blade will do fine. For the "island" portions of the 'A', 'R', and 'O', I stretched dental floss across the openings (any strong thread will do), and scotch taped the pieces into place held by the dental floss. Thread or dental floss won't show up in the final product. Then I cut a large opening in the lid of a paper box, and taped my stencil into it to make it rigid.

I did a couple of practice sprays onto cardboard, and then I placed the vests on a large piece of cardboard and sprayed EPOXY paint through the stencil onto them. Let it dry before handling! It came out surprisingly well, and the second one looks professional. They have survived a few washings, but I wouldn't overdo it.

For "In Training", I didn't want or need anything so durable. I bought a packet of "Iron-On Transfer" paper at Radio Shack. Unfortunately, it needs a left to right reversed image. Not having a "four dimensional rotation space" handy :-), I entered and sized the text in Windows Paint, block marked it, and did a reversal of the block. Then I printed it onto the transfer paper on an Epson dot matrix printer with a fresh "juicy" ribbon. Then I went over the letters with a magic marker to gets lots of ink on them. I ironed the transfer onto one of the vests, and onto the cloth cover that I have on Mac's prong collar.

The iron on transfer did not hold up well. In a few months it faded substantially. Now, only I can see where it says "In Training". So it worked out perfectly, that "In Training" faded out consistent with that ceasing to be relevant to Mac :-)