There are a number of ways. The easiest if you have access to water is to inflate the tube and put in a tub of water and look for the leaks. There will usually be some small bubbles trapped on the tube, make sure you wipe them off under water to insure that they aren't small leaks. If they reform without being taken out of the water, they are leaks.

Another way is to "kiss the tube". Inflate the tube so that it is much larger then it would be in the tire. It should be half again as big. Then slowly run the tube across your lips like you are gently kissing it. It looks silly but we humans have lots of nerves in our lips which is why kissing is so pleasurable If there is a flow of air you will feel it on your lips. Mark the place and patch it.

Another easy way to find a leak is to find the object that caused it. If you have a big old goathead sticking into the tire. That's your leak! Don't pull it out! Take the tire apart find the object and fix the flat. This is the best way since you don't have to take anymore of the tire off the bead then needed to get that section of tube out.