Prepare your trellis material and set it in front of you. You can use a metal rod or anything like a dowel rod to form your structure.
Heat up the center of the metal with a space heater or a welding torch. Let the metal sit in front of the space heater or hit the center a couple times with a blow torch.
Use gloves and a pair of work boots to bend the rod. Hold each end with one hand and pull up while you step in the center of the rod. Shape it as you wish.
Let the metal cool for an hour. Paint it if you'd like a certain color.
Attach the chicken wire to the rod using one of several methods. Wrap the wire around each end for a loose hold. Alternately, you could melt the wire to the rod using the blow torch again or glue it to the sides using super glue.
Set up your trellis in the garden. Place some vines and other similar plants under it. Pull a couple vines up onto the wire so they'll snake around as they grow.