The easiest route is to fake it with a texture map - there are some great wicker shader tools from Digital Carvers Guild, Shoestring Shaders and Inagoni. 

To actually model a basket, the Vertex modeler is probably the best choice. (although you could do it with the Spline modeler, you'd probably want to draw the paths outside in program in Illustrator) The horizontal weave is created by creating a circle of about 40 points. Then select every other point until 20 are selected and uniformly scale them down so that they all pull inward a ways. Next, sweep a "thread" of your choice along the path and then smooth/SDS the resulting shape. This will become your horizontal weave that you can replicate, rotate and scale to make the walls of your basket. 

Then it's just a matter off creating the vertical threads to match your walls and duplicating and rotating copies to creating the vertical threads. 

Just let me know if you need a visual.

Mark