I use really cheap, simple tools. You can get most of what you need in one handy little kit online. (Try poking around the Speedball store.) I like to print on random newspaper pages at first, both to test the print and see what random colors do to it.
I’ve been inspired by Frasconi: Against the Grain, a wonderful out-of-print monograph of the woodcut work of Antonio Frasconi, who emphasized that anyone could make block prints and that you “don’t have to go to a special place, with a lot of heavy equipment. This is something you can do in any corner of your home.”
Block printing is also a wonderful thing to do with kids. My oldest can carve safely, especially with the soft “speedy carve” style blocks. My youngest, who’s a little more cautious, helped me with the brayer.
I might find some good paper and do an actual run on this print. Sign up for my weekly newsletter to be the first to know when they’re available.