To start with, a good starting point is definitions

Lithoprints are traditionally done with soft stone.

Block prints are traditionally done with blocks of wood.

Linoprints are done with basically big rubber stamps.

All of these work on the idea of carving out a negative of an image, rolling ink onto the carving, and pressing paper over it to transfer the image.

I would suggest starting with linoleum. You can get carving tools for pretty cheap, I use something similar to this. Each blade does a different kind of cut at a different depth. Finesse comes in with pressure and angle and practice. I'm a big proponent of playing around, maybe wasting a block or two getting to know your tools.

And for practice, I would direct you to hunt down something like this. These carving blocks are great, they're really soft, double sided, and take pencil really well, which means you can draw out what you want (very loosely, just the basic idea), and press the graphite to the pad, and it will stick with a little pressure.

Speedball has some very affordable, water soluble inks for block printing, which makes cleaning your block (very important) a lot easier.

After you have something carved, I suggest trying different methods of ink application. Some people use rollers, some people use brushes, some people use sponges, you just have to find what works for you.

There are also a lot of different ways to apply the ink to the paper. Some people use very fancy lithoprint paper, and sometimes you have to get those wet, but sometimes you can do it dry. Some people use a press, some people put the paper on top and lay it over the block, and on and ond and on.