I took the technique from Crafty Containers, which has instructions for this plaited technique using strips of cardboard or folded pages from a broadsheet. I had neither to hand, but I did have a lot of pages that I was discarding from old home design magazines and a pile of Food Illustrated from Waitrose which I enjoy but don't keep.
The key to the size of the base is the width of the strips and how many strips you criss-cross at the start; I did 6 by 6 and this made a base roughly the size of a CD case. The strips were made by folding a magazine page in half, then in half again and then in half again - always lengthwise to get the longest strip. It would be neatest to fold the two sides the middle for the first fold but I didn't bother. For strength, I used the Food Illustrated covers for one of the strips in each six; I cut these in half lengthwise and folded them twice so they were the same width.
The length of your strips dictates how tall the basket will be. One page isn't nearly enough so I started by taping two strips together for each of the twelve starting strips. I added at least two more pages to each page and probably three or four. You could be neat and do this with glue; I used tape - I overlapped the ends of two strips and put one fold inside the other and tape to hold it. You can tape more than two strips together before you start, but the long ends can be awkward to deal with.
I'd recommend getting the book for step by step pictures - and several other techniques and lots of photos of what you can achieve, because it takes a while to get your head around how the base turns into the sides.
Take two cover strips and put them at right angles - don't make the middles quite meet as the join is there. You can staple them together (I didn't). Weave the other strips next to them to make a square of six strips. Use staples or pegs tat the corners o keep this together and push the strips close together without gaps. Draw a square from the midpoints of each side of the square - so a diamond inside the woven square (if you were using cardboard you would score the edges). This is the line you fold up along, so you're folding up a triangle of woven strips on each side. I folded a magazine cover to reinforce the base and used that to fold against.
The strips that were in the middle and are now at the corners go over each other to join the sides into one round and you go round interweaving them and joining on new strips. You may need someone to hold the basket up while you join on a new strip if it's not sitting perfectly flat on its base.
Peg frequently to keep things together (unpeg when you weave more). Keep the weave even - no gaps and try not to pull too much as this forms the circular shape and straight sides - or not, in this case. It's easier to bend the strips gently to get them over each other than to hold an end and weave it in and out - I think it's good not to put any creases in the strips to keep them strong.
When the basket is tall enough, you need to neaten the edges; you can bend a wire coathanger and make a circle to reinforce the rim and do the folding-in over that but I found the pages where stiff enough without it.
Fold one of the strip ends back and tuck it into the weave - you need to follow the weave and bend one strip forward and one back for each triangle point and weave in half the strips on the outside and half on the inside. You can be methodical and do all the outside ones first and then all the inside ones or just go round as you feel like it... I cut some ends short when I didn't want to lose the colour of the existing strip; often I folded the end to a point for easier weaving and to make it easier to leave it tucked behind another strip. Make sure every strip is held down by another strip to form a neat triangle at the rim and tucks in firmly.
I had planned to also weave strips cut from a plastic milk bottle in and out to strengthen the basket but it didn't seem to need it.
If your basket is somewhat uneven it adds to the charm! They say... And you can push and prod it to even it out, but this is best done before finishing off the rim.