You could look into a solution involving Paint Effects. Create a bunch of NURBS curves approximating the shape of the string in the net, then select a string-like Paint Effects brush and use the 'apply brush to curves' command. Should be pretty painless, and will give better results than an alpha-mapped plane.
That being said, if you want to go the texturing route, you just have to map something to the Transparency attribute of the poly plane's material. You could use a file texture or a simple grid procedural.