When these things become patterns or one becomes secretive about habits and schedules this is when the red flags become prevalent to the other spouse and we all know who our worst enemy is when we start thinking about why have things have changed, it is us.  Our mind starts wandering, assuming and when that happens it builds hysteria, paranoia and self doubt.

Spouses than start questioning things to themselves and when they can not cope with it they want answers on their assumptions.  Some of you will confront the spouse and usually what happens is there is denial or they are cheating and they tell the other one they are pretty much crazy.   So than the other one that confronted begins to think well maybe I am over reacting and this has two outcomes.  The other spouse will either be more forthcoming and maybe even admit an affair of some kind, or they will be on high alert that you are on to their activities and will become more elusive and tend to try and get away with their activities under the radar.
Because you have kids and you feel they would be better with you since the other spouse is having an affair, so than it becomes a custody battle also.   
You hire a Private Investigator and are convinced he or she will find something.
You will ask can you see their text messages? Answer is no, only law enforcement or you the spouse will be able to get those.  A subpoena is required in most cases to get the telephone records.
Can you put a GPS on their car? No only you the spouse can if you are on the title also and law enforcement. A credible private investigator will tell you that they can not do this as it is against the law. So these are things you should not ask for private investigator to conduct.  
What are some common characteristics of people that are having an affair? Disclaimer this does not mean your spouse is having an affair. 
Some of these have been mentioned earlier.  But the first one I usually hear about is that they are very secretive about their cell phone all of a sudden when in the past they were not. 
They have to work late or go out of town when they did not before and do not have a justifiable answer why they are working later or on weekends out of town.  
You catch them talking to an old friend on Facebook or other social media. In this day and age were all well aware of the scenarios.  
They say they are working late, so you drive by their work and they are not there. You call them and no answer.  
They are sneaking out of the room when they get certain phone calls.  The assumptions and characteristics are endless.  
What should you do?

First of all you need to ask yourself some questions and these are hard introspective questions. You need to be honest with yourself. 
Do you want to save your relationship?  
Do you want to know the truth and if they tell you they are not having affair will you believe them?
They do confess to having an affair but state they are done with it and had made a mistake. 
Will you both agree and can go to counselling maybe?  Will this bring out all the ugly truths because it may get worse before it gets better?. 
Are you going to be  able to forgive them? 
Will you be able to trust again after you have possibly rekindled your relationship?  This will be the biggest issue  because you will always have this in the back of your mind.  
There is not one solution that fits every couple.  Conclusion

Maybe you hire a private investigator and he or she finds the answer for you.  But one way or another this does not bring closure or trust in the end than what do you do? Maybe the investigator is not able to find the smoking gun due to unforeseen circumstances in the investigation.  These things happen so than you possibly mad at the investigator and they are out their doing what they can but have to follow the laws and keep their integrity also.  
So maybe if you do not get the answer you wanted and you start to seek other solutions in trying to keep your marriage and relationship you start seeking other guiding sources and avenues to solve the problem with dignity.  So that is why I am offering other resources also because I am not a marriage expert as a wise man has told me you will not be an expert at anything until you possibly 6' under .  You should consider all avenues and do your best to keep an open mind in these unfortunate events or assumptions that are quite common and you are not alone what you are feeling.