1. First, you need to ink your stamp (Stazon works great, but honestly, I use my Versafine Sepia because I like the color better. Use what you like, just be careful and let it dry).
2. Then use your heat gun to heat a piece of craft foam until the corners start to bend slightly, then heat the other side. I prefer to do it near an open window, in case of fumes (I didn't notice more than with embossing powder).
3. When the corners start to bend again, immediately stamp your image into the craft foam and wait a few seconds before removing the stamp.
4. Allow to cool and dry before fussy cutting the image out.
Tip: You can use any color of craft foam, but a light brown will give you a "true" faux leather look (especially when used with brown ink).
Here with grey craft foam :
Tip: You can use either clear or wood stamps (the teddy bear above is made with a clear stamp while the hearts are made with a wood stamp).
Don't forget your sentiment stamps! They look beautiful, as well.
Tip: It's easiest to use a stamp that you will be able to cut out using a shape die (e.g., a circle), because it can be tricky to cut fancy edges with a clean look (but it's possible: I did it with the teddy bear and the hearts, above).
Tip: All craft foam sheets aren't of the same quality. Some seem to be better for this letterpress look than others. The most important thing to do is to stamp immediately after you heat the foam, which is why you need to have your stamp inked, first.