The key labware or testing vessel of HTS is the microtiter plate, which is  a small container, usually disposable and made of plastic, that features a grid of small, open divots called wells. In general, microplates for HTS have either 96, 192, 384, 1536, 3456 or 6144 wells. These are all multiples of 96, reflecting the original 96-well microplate with spaced wells of 8 x 12 with 9 mm spacing. Most of the wells contain test items, depending on the nature of the experiment. These could be different chemical compounds dissolved e.g. in an aqueous solution of dimethyl sulfoxide (DMSO). The wells could also contain cells or enzymes of some type. (The other wells may be empty or contain pure solvent or untreated samples, intended for use as experimental controls.)
A screening facility typically holds a library of stock plates, whose contents are carefully catalogued, and each of which may have been created by the lab or obtained from a commercial source. These stock plates themselves are not directly used in experiments; instead, separate assay plates are created as needed. An assay plate is simply a copy of a stock plate, created by pipetting a small amount of liquid (often measured in nanoliters) from the wells of a stock plate to the corresponding wells of a completely empty plate.