This is the best way.... its easy to catch some one....begin to act weird.... like something is up....then after you have been acting strange ..... be forthright and confront....though you may not be sure this person cheated...you have to act like you know...but dont confront until you have enough feeling in your gut to be able to be certain they cheated... once you confront them if you still have that gut feeling and they say "no" and they "dont know what youre talking about"...... keep going....tell them you know and that they might as well stop lying....if they reply with "who told you that" or they start guessing...then its obvious they cheated... they go straight to the convicted person...typical... so the way you caught that person: is by them admitting to it unknowingly......so i hope this helps you catch the cheater.
Another Answer

Here are some ways to catch someone cheating. Note that these might not be legal in all jurisdictions.

Check Phone Bills
If they have a cell phone, you need to take a look at the call log. Look for numbers you don't know. Also, check your home phone, if you don't have the details of the calls on your home phone on your bill, request it. Also check cell phone bills.

Analyze the numbers and data. If they call you and find out where you are at then they call another number after every time, call that number.If you can get a voicemail great because their name will most likely be on the voicemail.
There is also the option of using spy softare to track cell phone usage data. In the end, proof like this will be important. Make sure you're positive they're cheating before taking this approach though.

Follow Them
Hire a detective to follow him or her, or follow them yourself one night.
Get a day off from work or your normal routine on the days your SO usually calls that mysterious number by reviewing the phone bill, but don't tell your SO. Borrow a good friend's car that your SO will probably not recognize or pay attention too with tint and sit there within view of of your SO's car and pretty much stock them if they leave and follow them. Take pictures if you see anything out of line, but don't reveal yourself.

You can hook on a car tracker which maps out everywhere someone's vehicle has been also. If you see him or her going to a woman's house or hotel ask him or her about what they did later. They will lie of course. It would be even greater to watch which hotel room they go to and go cover the peephole and knock on the door and have them open it. If they know you are out there and won't leave or answer the door and they have a cellphone and you have one call it and listen to it go off inside the room. :) IF it is a other person's house or apartment and he/she answers already have your cell ready and call it as soon as they open the door and BS's about your SO is not there call it and listen for the ringer going off around the corner of the hall way. Your SO will poop their pants. If they say they aren't their even though you saw them go int there and If you feel warrated spray the person cheating with your SO with a pepper spray fogger and fight past them into the house or hotel room you saw 100% your SO go into and catch them in there.

Investigate Computer or Internet Use
Look on the internet for signs a spouse is cheating. You might buy a keylogger. Never let them know you installed it. They may not even communicate with their other lover on the computer though. If your SO uses the computer a lot though this one is good and produces evidence you can even print out. They may be at work when they use their email account but once they log on from home even once you have their screenname and password and can check their account anytime. It takes about five minutes to install and cost me about $40. You see everything. Web page screenshots, every key typed, every website visited.

Look at Credit Card Statements
Look for receipts or charges on a credit card for dinner or lunch for two, or hotels.

Semen Detection Kits
If you are a male and don't regularly have sex with your SO you can buy checkmate which is a home semen detection kit cost about 45 dollars and takes 5-10 minutes. You can tell what those white stains in you girlfriend's underwear are. (Women, don't use it on your man's underwear. I can tell you cause I am a man and might have a little semen in my drawer and I don't cheat.)

Surprise them at Work
Bring them lunch at work unexpectedly and be friendly to all his/her co-workers giving them muffins and pasteries. This does a lot of things. It lets the other people know your SO is taken and in a relationship. The people in the office will know he or she is taken and will be watching them. There is always someone in the office who has been cheated on in the past ,or unsuccessfully hit on your SO, or plain just doesn't like them and will try and expose them. Your SO will have to try to keep it underwraps more and use the cellphone and other means giving a paper trail. Having a friend in his office is good, but beware of them also.

Look Inside
Look at the reason why you are suspicious. Are you doing something wrong yourself. Guilt is a powerful thing. My buddy's girlfriend who was cheating on him was always suspicious and accusing him and since he was my roomate, I know for a fact he wasn't cheating on her. Then he got suspicious becasue she was always accusing him and he caught her. Now she isn't his girlfriend and he has sex with her and lots of other women and he has the right as far as I'm concerned. He was faithful to her and didn't take the numerous oppurtunities thrown at him. Now he just has fun.

Are you just plain unhappy with your relationship and want out? Maybe you don't want to be the bad guy and break it off and want a good reason too other than you are just bored with them or don't love them after all the things they have done for you. Maybe you already have your eyes on someone else and desire them even though you haven't cheated. Be completely honest with yourself and what you want and the true reason you are suspicious.


ANSWER

Frankly I think if you know someone is cheating it is not worth the time and effort (nor are they) to catch them - just pick up and leave. Another chapter closed. Why do you suspect they are cheating in the first place? that will lead to your answer...