Perhaps the easiest way to start any stake and strand basket is using a solid wooden base.   In fact it is quite common to use wooden bases when working with cane but they can used effectively with willow and in some situations they are more functional than a woven base.   Today, the most readily available material is plywood which can be cut to any size and shape, but you can solid timber if it is available.   Interesting bases can be made by cutting thin "logs" from a tree but a lot of care is needed to prevent them warping and cracking as they dry.   In fact quite a lot of time can be spent preparing this type of base especially if you sand and french polish the board if you were making a tray perhaps.   Even a simple plywood base will benefit from a bit of preparation.   I usually sand the base smooth and then apply a coat of stain followed by an application of teak oil.   I find this gives a pleasing effect even to cheap plywood.   Solid bases are useful for trays, bottle baskets and even log baskets where they tend to stop the "bits" from the logs from falling through to the floor but the main advantage is that they can be cut to any shape.   It is even possible to use irregular shapes like drift wood where instead of doing a foot border you just drill the holes and glue or pin the stakes into the base.
Start of by cutting you base to size and then mark out where the holes have to be drilled.   Spacing the holes can be quite a problem and I use a sheet of paper as a template to get the spacing correct.   For a willow basket I space the holes from 1 to 2 inches apart depending on the thickness of the willow and the size of the basket.   If the basket is square then you can drill larger holes at the corners to take your corner posts.   Drill carefully through the base on to a piece of scrap wood to save the drill damaging the underside of the base.   Once the holes have been completed you can sand and polish the base as you require.
Insert some stakes through the base holes so that about 6 or seven inches protrudes to the bottom of the base (this amount depends on the spacing of the holes but will be apparent after the first stake is bent into position.   If you are using willow as stakes you can thread the rods through starting with the tip as some of the but ends might be too thick to pass through your holes.   I thread my rods through in this manner as it tends to keep all the stakes the same thickness.   Take one of the stakes and bend it down at right angles (flat against the base) then take it behind the next stake to the right and in front of the next two leaving it on the inside of the base.   Treat the next stake to the right in the same way and so on until you have only three stakes left standing. These must be woven though under the first stakes following the pattern.   This is made easier by easing these first stakes up from the base to allow the last ones to be threaded through.   When you have completed the staking up pull all the stakes up from the top side of the base to make the base border tight and even.
If you are using drift wood or irregularly shaped stumps then you must drill holes 1 to 2 inches deep and glue the stakes into position.   You can get really good glues from boat builders which set in contact with moisture.
The square basket at the top of the page has been made using a square plywood base.  The sides are french randing using buff and brown willow and the corner posts were made from 3/4 inch dowel..