To get an accurate measurement you need a caliper, but if you take an old spoke to a bike shop they can match it for gauge and length. Most spokes are either 14 or 15 straight gauge. There are also spokes that have 2 sizes on the same spoke. These have thicker material on the ends and thinner in the middle. People who are weight conscious use this type.
It's not enough to just know the diameter of the spoke. The length is equally as important if not more so. If you buy a spoke that is too short it won't lace up. If you buy one too long it will puncture your tubes. Almost every hub and every rim will require a different size. Rear wheels requires two sizes because of the gears.
Wheel building or repairing is not difficult, but it does take a little knowledge of how they are made. There are web sites that deal with this in much better detail. But if you'll check past questions and answers you'll find some good info right here on the Forum. The main thing to remember is that you need to know BOTH the gauge AND the length.
By the way, lenght is measured in millimeters. Stainless steel is the material of choice. There are cheap zinc spokes but avoid them if you can. These kind are often measured in inches. Good luck.
Wow, thanks for the excellent info! I just got so frustrated with the shoddy work my bike shop was doing I just figured I HAD to learn this stuff. In my opinion, the ONLY reason to use a shop is for maintenance. When they can't manage to do that, adios. Thanks again.