Tablets – thin cards approx 6cm square with holes in each corner, can be made of sturdy cardboard, timber, horn, leather, bone or even metal. But cardboard is fine to begin with. Rounded corners make turning smoother and the cards more comfortable to handle.
Yarn – the warp threads in tablet weaving (the long threads which are threaded through the tablets) must stand up to high tension and a lot of friction from the tablets being turned. Wool, silk, linen and cotton are all options, I work in wool usually.
Loom – it is possible to weave by tying one end of the warp to a fixed point with the other end tied to your belt, but a simple loom consisting of a piece of timber with doweling fixed into each end makes it a lot easier to manage, not to mention easier to walk away from for a break. The dowel needs to be very firmly seated to cope with the high tension on the warp threads. A longer loom allows you to weave more before having to move the work up and re-tie the warp.