Hiya, so sorry you are going through this.
I am with the camp that thinks if you suspect something iffy is going its very naive to go in there and "talk" to your partner about it. By doing so you lay all your cards on the table against someone who potentially is a very sneaky and sly individual unlikely to offer any kind of opening up and honesty to you. They are then tipped off, they change their behaviours from what you have told them makes you suspicious. They are even more careful and in the long run you are less likely to ever find out the truth or certainly a lot lesser extent of it. This is ofcourse ASSUMING there is something untoward going on.
I have been down this route sadly. And also very sadly have now helped numerous friends in situations like this.
Firstly if you do not want to be caught in any circumstances start by taking low risk methods. Things like, watching mobile phone behaviour - if when looking at their mobile, have a pre thought out excuse for you being in possession of it if you get caught. Look at bank accounts, cash withdeawals, statements - any suspicious, more cash transactions, restaurants etc. Check EVERYWHERE for condoms (esp so if not used between yourseleves) - pockets, wallets, car. I have discoverd condoms in the car in the boot behind where the panels are removed to fit new light bulbs into the rear lights, a friend found a little box under some floor boards in the house!!. In fact search everywhere in the house for anything suspicious - in pockets in clothes in wardrobes, amongst any of his hobby stuff, garagesm sheds, another friend discoverd receipts, a sim card and other incriminating stuff behind the bath panel in her bathroom!
It can be bloody dreadful if and when you find something cos it hurts and also if you dont you can feel like you're going mad at times!!
Until he knows you suspect - you have the upper hand. You can monitor all of his behaviour. Look out for texts in middle of night, perhaps pop downstairs late at night for a glass of water (or something) if he is down there on the PC late at night. His reaction to you suddenly being downstairs that late if you are usually in bed can give a good indication as to what he may be doing on the PC. I did this but he always have another window open (to quickly click on to cover up his MSN chatter)on an innocent website - I became suspicious after several night time visits down stairs he was ALWAYS on the same innocent website homepage!!
What ever you do, where ever you look always have a pretty genuine sounding excuse for being/looking where you are incase you get caught. For example, when I decided to rifle through OHs wardrobe and every pocket in there I tidied it, so I had a reason to being in there. I found phone numbers with no names on scraps on paper in a suit jacket or 2. I copied the details instead of taking the actual scraps - cos I suspected he would check after he realised I had been in the wardrobe.
Obviously as others have also mentioned there are things you can do with the mobile - so he txts you etc, but persnally I would not risk that until you are ready to confront the issue incase it all backfires and you get "caught".
Computer history is one to keep an eye on too. Cheaters will nearly always delete it BUT they do occassionally slip up, so its checking it frequently. Also, try and find email passwords - not so easy. Also be aware that he may have a whole new Email a/c exclusive to his affair (if there is one) that you will not know about. Again - this may only come to light by regularly looking at his pc.
You can purchase spyware and I am crap with IT but a few friends have said its been worth every penny and really useful in getting the WHOLE story and not just the bits their partners feel forced to tell them when the shit hits the fan.
All in all dont expect answers over night, it could take a few weeks. Try not to let it obsess you as well - easier said than done.
I am not saying THIS method of action is right or the best thing to do but merely sharing my experiences, and offering some advice, so IF this is the route you wish to go down, I hope I can have helped.
I hope you dont find anything awful but good luck in whatever course of action you decide to take!