Before any of the blocking methods, this is what you need on the table. Most of it is ordinary household stuff.
Lukewarm water in a bin, tub or plugged sink. A surface you can pin into, which can be a bed, cardboard, the carpet, foam blocking mats or a cheap yoga mat. T-pins and a measuring tape. A towel big enough for the garment. A rinse free wool wash if you want it, and for some methods an iron with steam or a steamer.
The next segment covers wet blocking.
1 Lukewarm water
Use tepid water, about room temperature. Too hot or too cold shocks the fibers and can felt them. A plastic bin works. So does a bathtub or a sink with the drain plugged.
2 A surface to pin into
You need somewhere to stretch the wet fabric out and shape it. A bed, a piece of cardboard or the carpet all work. Interlocking foam blocking mats are made for this but cost more. A plain yoga mat from a big box store does the same job for about a tenth of the price.
3 T-pins and a measuring tape
T-pins hold the fabric to the surface. The measuring tape is how you check you have hit the dimensions on your schematic, which matters most for sweaters and shawls.
4 A towel
Big enough to lay your garment in. Some blocking methods use a towel to take the first of the water out before you shape the piece. If you block on your bed, put a towel under the fabric too. A wet bed can take three days to dry.
5 Rinse-less wool wash
Optional. Think of it as conditioner for your fabric. It helps the piece last longer and it smells nice. You do not need it the first time you block something, but it is good when you wash a garment later and block it again.
6 An iron with steam
Some blocking methods call for an iron. One with a steam setting is what you want.
7 A steamer
One of the best tools for blocking. An iron will do, but a dedicated steamer is worth it if you have the means. They run from about twenty dollars to three hundred for a professional model, and they are what gives a garment that finished look.