Choose one sheet of a neutral color of construction paper like brown, black, or white. This will be the base of your basket. The other two sheets can be any color of your choice. This will form the decorative sides of your basket. It can help to use a ruler or other sort of guide so you can your paper in straight lines.
Repeat with a total of eight strips. The finished base should have a 4" x 4" woven square that fits just inside the lines you drew on each strip. In other words, you should have a square that has eight strips sticking evenly out 3. 5" on each side.
It can be helpful to put a 4" x 4" box or block of wood in the center of your basket and fold the strips up against this block. This will make the next steps easier.
You will need to use approximately one and a half strips to make it all the way around the basket. You can simply tape or glue the two pieces together. Try to place the connection so that it comes on the inside of the basket and is hidden by a strip from the base. This will give your basket a clean, seamless look. Weave the strip all the way around the basket. When the two ends meet, tape or glue them together, hiding the tape in the same way.
Keep repeating until you reach the top.
If you want to add a handle, simply tape or glue each end of a long strip of paper to opposite sides of the basket before you add the top panel.
You will need many tubes of paper, so repeat this process for each. In place of a wooden skewer, you can use a thin knitting needle, a 3mm dowel, or anything similarly long, narrow, and round.
You will need to use more rays for larger bases. The closer together the rays are, the tighter your weave will be.
Leave a heavy weight on top of the base while it dries to make sure that everything is nice and secure.
As you weave, the rolled tubes will flatten out. This will make your basket stronger.
For each ray that stands on the outside (the last tube you wove past the ray went to the inside of the ray), fold the end over the basket and glue it to the inside of the basket. Use a clothespin to hold it in place while the glue dries. For each ray that stands on the inside (the last tube you wove went outside the ray), fold the end over the basket. Instead of gluing these to the outside, tuck the end inside the woven basket at the second row from the top, securing it in a way that makes it fit into the weave of the basket.