It is very difficult to get anyone to admit that they are having an affair. People will not usually admit to an affair unless they are pushed into a corner and they really have no choice. The only way to do this is to confront him (or her) with evidence so strong that they can't deny it.
You can push your spouse into this corner in a number of ways:
Pay a private detective to follow your spouse, and record evidence of the indiscretion. Then confront them with hard evidence.
Tell them that their best mate has already told you about the affair and it would be pointless to deny it.
Tell them that they had been talking in their sleep and that you know everything, except the name.
Tell them that if they don't admit the truth or give an explanation you are going to leave their entire magazine collection of porn on the parent's doorstep.
Tell them that you have already done it to them so they can admit the truth (this can be a bit dangerous if you happen to be wrong about the affair) Whatever happens, hopefully you can give each other the opportunity to talk things through...
Ask them to take a lie detector test. This can be difficult if you don't have access to a good machine. Sometimes asking them to swear on a loved ones life can work. if there is hesitation, then you have your answer.
Get a key key' monitor for your computer. This is a hidden application that runs in the background when the PC is activated and it records every key stroke made on the keyboard. This one has caught many a cheating spouse and when presented with the hard evidence they just can't deny it.
Keep a check on bank accounts and receipt purchases. Search pockets and keep an eye for different color hair on clothes. Collect all the evidence and confront them with it.
When you have finally realized that your spouse is cheating on you. Don't make a confrontation with your suspicions until you have the hard evidence. People who cheat are very clever liars and will wriggle out of an accusation very easily. Ultimately the best thing to do is to try and find out who the other person' is and go and talk to them. Chances are they will know nothing about you and will be just as angry as you. Then you can both get him to admit it.