I am really into personalizing. I try to make most things I use. I have been carving stamps for over a year. This same technique can also be called "linocuts" or "block printing". I reserve those terms more for large scale artist prints. Which can be very detailed and amazing. Although making my own stamps is amazing, I like to just call them stamps.
I like to use Speedball products. I picked them up at the Michaels store that I work at.
I am sure that these tools can be purchased online if you have trouble finding them.
Speedball carving tools
Carving block (these can be brown, pink, white or ivory)
*****You can also carve those white vinyl earasers
Decide the size of your stamp. Sketch the design in pencil on a piece of paper.
***NOTE: you can draw directly on the block, BUT it will be reversed when its used AND its hard to erase if you mess up.
Cut out the design. Use the back of the carving tool to burnish the design onto the block.
Use knife and gauge to carve out the negative space. I like to work with a piece of paper under my block so I can easily get rid of the scraps. It can get messy. Rinse your block to wash off all tiny bits.
***NOTE: you can also carve out the positive space for a more solid block effect.
******NOTE: do one or the other
Ink the stamp test it. There are may be more you need to carve away that you won't see until you test.