How did you find out that he's cheating?
Is it hearsay or gossip from friends?
Or do you have hard evidence like the smell of her sweat on his body, or you've caught an STD and there's no other way except via him?
Before you decide whether to bring it up, consider the possible outcomes.
a) He admits it.
- You ask him if he used contraception & if so what kind. If no condom you ask her medical history of STDs. He probably won't know, but it will drive home the level of irresponsibility and risk.
- You have an emotional reaction - possibly fear of losing him - and possibly cover that up with an angry and judgemental outburst. At the very least, you now know that you can't trust him to be faithful, although at least he has owned up to the truth - which is a significant and good thing.
or
- You ask him how he feels about her, how serious it is, and whether he prefers to keep seeing her. Then you make a decision whether to stay on knowing that his love and attention is divided, or you decide to split.
- You ask him to choose between you and her, with the proviso that if he chooses you, it will be on the mutual agreement of staying together as a monogamous couple. If he chooses her, you pack your bags, and ask to stay with family or friends until you can find a new share house or place to rent. Or he packs his bags and leaves.
b) He denies it.
- If it's gossip, invite the person who told you to come over and repeat what they said to his face. Regardless of what gets said, double check everything with the relevant person. Sometimes people lie about affairs for reasons of their own - [this happened to me 44 years ago - envy can make some people deceptively nasty and cruel.] Keep talking until the truth comes out.
- If you have hard evidence, then his denial compounds the deceit and validates any distrust you may feel. Few relationships can survive that, so you suffer less in the long run if you end the relationship and leave.
c) He denies it
and it turns out that there was no affair.
Either the gossip lied or misinterpreted something,
or you have misinterpreted what you thought was evidence
but it turned out that there was another explanation which was easy to prove.
In this case, you apologise for having doubted him, and you take a good hard look at what caused you to go snooping in his mobile phone.
If you have feelings of insecurity about yourself or doubts about whether he loves you - talk about these with him. What specific actions cause you to feel loved? Do you like him to ask about your day and listen with empathy and warm feedback? Do you like him to bring you breakfast in bed on the weekends? Would you like him to leave surprise notes and messages of love in unexpected places?... Let him know what you need.
d) If he decides to end it with the other girl, ask him what you could do to help him feel happier and more fulfilled with you.
Make sure it's a list of specific, do-able actions. Take on doing as many of them as you can, but only if it is sincere and brings you equal joy.
Encourage him to be more open about his feelings by listening and validating, never criticizing.
If the problem is over familiarity - add new interests and adventures into the time you spend together. Invent welcome surprises for him.
Look into learning better communication skills, learning them together if possible, but unilaterally if that's the only option. On communication skills, there are many free blogs in Psychology Today and videos online, books in local libraries, and free local practice groups in many areas.