Is it nylon, silk or lace? Either way, you need to fasten it into a porous bag like those net bags you can get for putting tights in the washing machine....but bigger. A white pillow case might suit. Then, make up a solution of washing liquid for delicates - the stuff that is for net curtains will be ideal. Squeeze the bag gently several times and if necessary change the solution and repeat - DO NOT WRING JUST SQUEEZE. Then several changes of clean water, squeezing out, to rinse.
Lay out a couple of big bath towels on a clean floor and put the bag onto it. Roll up and step lightly on to squeeze out excess moisture, repeating with dry towels if needed. By the time you empty it out, the veil should be almost dry. Leave it flat to dry. Don't become disappointed if it tears - old net can get brittle and you can only do your best. Bear in mind it wasn't originally intended to last very long.