First load up Photoshop then File->New, or Ctrl+N. Create a new document 400 pixels by 400 pixels. Mode: RGB and Contents: White.
If you have a background layer, click the New Layer button on the bottom of the layers box - - Then delete the “Background Layer” (Right click -> Delete Layer)

Fill in with white/black and Press “D” to put the colours back on default and then Filter->Noise->Add Noise. Set the amount to 400%, distribution: Uniform and check the “monochromatic” box. This box makes the “noise” created all one colour, or black in this case because our foreground is black.

Then Filter->Pixelate->Crystallize. Set the cell size to 10, but in a larger image it will need to be larger. Just to clear it up a bit and make it slightly more blurred, go on Filter->Noise->Median and make the radius to 2, 3 if you want. At this point you should be so far:

Filter->Blur->Motion Blur will create the weaving straw effect. Put angle on 0 degrees and distance as 40.

Then do Filter->Brush Strokes->Accented Edges to make the edges a bit clearer.
Edge Width: 3
Edge Brightness: 30
Smoothness: 3

Now you should be here:

To finish off the effect colour it by selecting your layer and pressing “CTRL+U”. Check the colourize box and set both hue and saturation to 35. This puts on your brown straw colour:

If you are happy with this you can stop here. However to add another pattern weaving inside this, duplicate the layer (Right Click on the layer -> Duplicate Layer) Select the bottom layer and go to Edit -> Transform -> Rotate 90o CW. This rotates the wicker around perpendicular to the horizontal one. Select the top layer and in the “blending mode” in the layers panel and choose (below darken in the 4th section) Or go to Blending Options by double clicking the layer and in the general options change the mode to lighten.