There is special rubber around for making your own stamps with but I find erasers to be a much more affordable more easily obtainable material. They come in various sizes and are plenty big enough for basic simple stamps. I like to use the Woolworth Jumbo Erasers, but they went out of business and I'm going to have to do some experimenting with other brands soon as my stash is running out. You will need to get the "proper" stuff if you want to make a large or intricate stamps.
Linoleum gouge tools are the generally recommended carving equipment. I couldn't source any locally when I was starting out and have a small set for wood carving instead. They cope with the basics and the rubber erasers fine. They come in different shapes. The main ones I use are a V shape for detailed work and a U shape for removing larger areas of rubber. The smaller your gouge the finer your detail will be.
Draw a basic shape onto the surface of the rubber using a pencil.
Using your V shaped carving tool at an angle of about 30° gently scoop out the outline of the shape.
Test your stamp with an ink pad and some scrap paper. Personally I like the rugged look of the extra bits showing on the stamped image, if you prefer a cleaner image then gently remove the unwanted portions.
I wanted to add some pattern to my shape rather than leaving it solid.
Using the V shaped tool carve out a pattern.
Test it and continue until you have the desired result.
Each eraser has two sides so I normally make my stamps double sided.
I repeated the heart shape with the V shaped tool in an echo pattern for the reverse of this stamp.
Have fun carving. If you like a rugged style and want to explore stamp carving further then this is a great beginners book: "Rubber Stamp Carving" by Luann Udell.
Blessings to you all from Angela