Measure the chair's seat if it is a simple square or rectangle, and write down those dimensions. If the chair has curved surfaces, however, trace its shape onto cardboard or brown craft paper, and cut out the shape, making a template of the seat.
Mark the seat's dimensions on an expanded metal sheet with chalk if you didn't create a template. If you created a template, then set the template on top of an expanded metal sheet, and trace around the template's perimeter using chalk or a marker to transfer the template's shape to the expanded metal sheet.
Cut the shape from the expanded metal sheet by using a metal saw.
Smooth the edges of the cut expanded metal sheet with a metal file or angle grinder.
Set the cut piece of expanded metal into the frame of the chair seat. Clamp it into place at a number of points to hold it securely.
Put on work gloves, a respiratory mask and a welding helmet. Weld the edges of the expanded metal piece to the chair seat's frame at a number of places with a tungsten inert gas (TIG) welder. Weld using slow movements around the edges of the metal. A tack-weld works well; it is a short, preliminary weld joint that can be broken easily if necessary for re-adjustment. Pull the molten pool from the steel filler welding rod onto the thicker metal of the frame, gradually drawing the molten pool to the expanded metal edges to prevent burn-through. Use argon shielding gas to keep the weld area free of contaminants from the air.
Verify that the expanded metal is in the correct position for the chair seat. Weld all the way around the edges to ensure that the weld joint is strong enough to hold the weight of a person. Allow the welds to cool.
Smooth rough edges on the welds using the metal file or angle grinder to prevent injuries and damage to clothing.
Apply a metal primer paint to the chair, and allow it to dry thoroughly.
Paint the chair the desired color with a rust-inhibiting paint for metal.