Determine if the coin is supposed to be 22K or 24K gold. Pure (24K) gold is extremely soft and easily damaged, so most coins are alloyed with another metal to harden them. There are some exceptions like the American Buffalo gold coin. To check a coin's composition look it up in any good numismatic catalogue such as those available online from professional coin grading services (see links under Resources).
Place water in a graduated measuring container (the type used in chemistry labs is perfect). Note the exact volume of water in the container. Now place the coin in the water. Be careful not to splash any water out. Check the volume reading again. Subtract the volume of water originally in the container from volume with the coin added to get the volume of the coin. For example, if you started with 25.0 cc (cubic centimeters) of water and you have 27.0 cc with the coin added, the volume of the coin is 27.0 cc minus 25.0 cc, or 2.0 cc.
Weigh the coin using a precision scale accurate to one-tenth gram or better (a typical chemistry lab scale is good).
Calculate the density of the coin. Density equals the weight of the coin in grams divided by the volume in cubic centimeters. For example, if the weight of the coin is 38.0 grams and the volume of the coin (from step 2) is 2.0 cc, the density is 39.0 g divided by 2.0 cc, or 19.50 g/cc. A pure gold coin has a density of about 19.3 g/cc (grams per cubic centimeter) if it's 24K gold and about 18.5 g/cc if it's 22K gold. In our example the coin is almost certainly real gold and probably a 24K gold coin.
Repeat the volume and weight measurement and density calculation to be sure you have reasonably accurate figures. However, don't be upset if you are a little off the first few times you identify real gold coins. If you calculate a density of over 15 g/cc it's probably a real gold coin and you just need to practice this technique a little.