I'd urge you to consider whether you have a valid case for doing so before going any further. It's quite likely that you'd also be breaking the law in whatever country you tried to do this.
The only time I can see this being acceptable is if you know the person you are targeting, and you were doing this in order to protect them because they were vulnerable for some reason.
Use the techniques outlined below with care, and only in the appropriate circumstances.
How to Check Another Person's Messages
If you have access to the person's phone, then it's possible to copy their messages across to a different SIM card or to memory stick. Then you can install that SIM card/memory stick on a different phone and read their messages at your leisure.
Alternatively, software such as Mobile Spy claims to enable you to intercept text messages. In order to use this software, the phone you want to check will need to be a smartphone, such as an iPhone or Blackberry. You will also need to have access to the phone you want to target for a minute or two in order to install the software.
Once it is installed, then text messages sent to the target phone will also be sent in real time to the software’s server, so all you need to do is log in to your account to see those messages. This will reveal copies of all text messages sent and the numbers they went to.
Since this is an app that is installed on the target phone, there is every chance that the phone owner will spot the software at some point and wonder what it is doing there. This is especially likely if they are an experienced phone user.
Although this software is questionable if used for the wrong reasons, it can be a great ally if you are concerned about your child talking to dangerous people, or if you want to check that an employee isn't misusing their company phone.