Reflective umbrellas are a popular way of creating soft lighting effects, especially for portrait photography. Here's a quick and easy guide to making a cheap DIY reflective umbrella, and still be able to use it out in the rain.
What You Need to Make a Reflective Umbrella
Umbrella. Small collapsible ones are preferable, if only for the sake of convenience and storage,though anything will really do. You won't be sacrificing this to the photography gods or anything: all you will be doing is modifying it in a way that will neither affect the waterproof qualities of the umbrella nor the aesthetic qualities, so you can use your usual umbrella for this without any fear of losing its functional purpose. If you'd rather not risk it, though, umbrellas are very cheap to buy, and you don't need a high quality one for photography.
Reflective spray paint. Most people go with gold (warm) or silver (cool), though other colors of reflective spray paint can be used for more unusual lighting and color effects. If the selection is available, try to go for a spraypaint that is especially made for use on fabrics, as that will last longer.
Old newspapers. You're going to be making a bit of a mess, and unless you want to risk getting spraypaint all over everything, having a large quantity of scrap paper is a good thing.
Construction of Your Reflective Umbrella
Go outside for a good, ventilated environment. You'll probably want to spread those newspapers on the ground and wear work clothes, just in case of paint splatter.
Open the umbrella.Positioning yourself upwind, begin spraying the concave underside of the umbrella. Make sure every bit of fabric is thoroughly covered, but not so saturated that it soaks through and colors the other side. It's okay if there are some drip marks and the paintjob isn't especially smooth: small imperfections will not make a noticeable difference in the reflective qualities of the umbrella, and thus won't effect the photography.
Once you have this done, leave it out to dry (but make sure it doesn't blow away!) After, try it out: Is there enough of the reflective paint on it to properly bounce light? If not, another layer of reflective paint can be added. Repeat until the reflective umbrella will suit your purposes—both for light, and for keeping the rain off.
More With Reflective Umbrellas
Of course, you're not done yet. In addition to the reflective umbrella itself, you also need a stand and a lighting source of some sort. There are a some DIY project ideas out there if you're in the mood to build yourself a complete set up, though they are, of course, also available for purchase for those so inclined. Otherwise, use of the buddy system, where you have some friends hold the umbrella(s) for you, will have to do.
In addition, you need to learn how to use a reflective umbrella in the first place. For a great beginner's overview of how to use reflective umbrellas, check out this article.
If it doesn't look like a reflective umbrella is quite what you're looking for, there are other options as well. Here's a guide to making a DIY softbox, or a DIY sheet reflector. There are many options available for potential reflective surfaces, each with their own unique effects, so experiment away!