To make a bridal veil, use low iron settings when ironing veil materials such as tulle and lace, and consider purchasing a veil kit from a craft store if you are not skilled at sewing. Use a rotary cutter for a straight cut on the fabric.
For a good idea on how to construct a veil, consider purchasing one from a thrift store to examine. You can also repurpose the fabric from the thrift store veil. Consider whether you prefer a shoulder-length, waist-length or other-sized veil. DIYNetwork.com provides a list of measurements of popular veil lengths sold in stores. Use a headband or hair comb for the headpiece. A hat is another option for a unique headpiece.