While there may be more than one right answer to that question, it all comes down to how efficient and effective each method is. There are some techniques that will give you a great return for your time in terms of valuable evidence, and then there are those that are very time consuming and don’t guarantee any returns at all.

Add to this the moral issues around some of these methods and you’ve got a lot to consider before you decide which way to go.
Here is one method that is very quick and effective:

Find out the make and model of your spouse’s cell phone. Next, go to the manufacturer’s website and download the operating manual. Study this until you know the phone inside out. You will need to know how to access the information as quickly as possible – In some cases you may only have a matter of seconds.

Take every opportunity you can to access your spouse’s cell phone. Your biggest opportunity to get the information you need is going to be shortly after they arrive home. With the knowledge you gathered from step one, you should know the phone well enough to quickly access the address book, incoming/outgoing phone calls, and the text message area. Make note of any strange text messages and write down as many phone numbers as you can. The key here is to access their phone frequently but only for a few seconds at a time.

Eventually, you’ll end up with a list of phone numbers that you can do a reverse search on. Start with the White Pages website (it’s free) and enter each number. The results should provide you with a name and address. If you’re not able to get information on a number, that means that it is either unlisted or it’s a cell phone number. In order to get cell phone information, you’ll have to use a service that buys the information directly from the cell carriers. There is a small charge for this service because the information is not made public.
Why does this work so well?

It works because your spouse will risk leaving their phone for a few minutes. Even if there is incriminating evidence on it, they would never think you’d have time to gather phone numbers and to read text messages – especially if they know you are unfamiliar with the phone’s functions.