A Dai is any stand or podium.
A Daiza is a carved wooden stand that fits the base of a stone closely.
A Suiban is a shallow water tray usually of pottery.
A Doban is a shallow water tray usually of bronze or other metal.
Many people new to the art wonder how the beautiful stands are carved. Below is a summary of the technique used by Sean Smith, a professional woodcarver who runs Custom Oriental Woodcraft. Tel. (717)957-4172 (With thanks to Jessie Edwards of the (South African) Eagle Eye Suiseki Society for the account.)
Place the stone on a rectangle of wood of suitable type, depth and with adequate clearance all around. Sean recommends walnut. Use a sharp pencil to mark the wood, where the edge of the stone will contact with it, meticulously.

Remove the stone and draw another line about a quarter of an inch inside the first. Use a router to remove up to this inside line, to the depth necessary. Use a dremel or similar, with small router bit, to remove the last portion - up to the first line drawn. Keep testing for fit, marking any portion to remove and carefully extending until a perfect fit is achieved. If this job is done well, the wood should fit the stone so that it may be lifted, as one, by holding the stone alone.

Draw another line parallel to the outside of the routed out hollow. The distance depends on the size of wall required. Use a scroll saw, fret saw or fine bladed jigsaw to cut around this line. It may be done vertically or at a slight angle so that the daiza slopes inwards from the top.

If this is done neatly, and care is taken to exit from the wood at the same point as you start, the scrap wood can later be used as a perfect jig to hold the work.

Sand the daiza using the smallest sanding drum on a dremel for speedy finishing of the irregular outside edge.
Put the stone in and decide on the position of the legs. Usually one at each end and one beneath the "centres of weight" of the stone. (The portions which look heavier.)

Return the daiza to the scrap piece and tack the jig to hold the work piece upside-down. Secure with a couple of very thin wedges, just enough to fill the saw cuts and chisel off the tops. This allow the router to be used for fast removal of the waste wood between the feet.

If a step in the wall is desired, turn the unit over (right side up) and tack it once more. Use a Dremel to carefully route just outside the top edge to achieve the stepped effect wanted.

If the feet are too deep they can be cut on a circular saw, but this is a dangerous undertaking. Alternatively, but more laboriously, sand them down to size on a large sheet of sandpaper held flat.

The feet can be shaped rapidly using the sanding drum on a Dremel. Final sanding should be done with progressively finer grades of paper all over, until no scratches remain. The dremel can again be used on the irregular parts.
There are several options for finishing. Use a laquer spray, which dries very quickly, or painted laquers which after drying should be cut back with wet and dry between each coat. A high gloss finish should be avoided. Build up the finish until you are satisfied with it. If the end result is too shiny it can be dulled with steel wool. A more natural finish can be achieved with beeswax polish or similar.