Forgiving happens naturally. The feeling grows out of nowhere because in order to move on, you need to forgive.
But do I need to forget about it? Do you? Well, some can forget easily and some couldn't. It all depends on how you view your life and what you want to achieve in your future. As for me, I get angry easily if I got betrayed especially by anyone who's close to me. And that never occurred to me for the past 18 years of my life till a few months after I turned 19.
At first, I was hurt. Then, every time the incident crossed my mind, I got angry and a little bit sad. I promised myself not to forgive this person until forever but guess what, I ended up accepting that person's apology. It felt nice. It's like this weight that I was carrying disappeared. But I never forget. Why? Because it's a lesson for me. The incident shall remind me that no one in my life last forever. No one will stay just because I wanted it that way. Life doesn't revolve around me. Therefore, I have to remind myself not to let my guard down. Ego exist for a reason so don't hesitate to use it.
Well, don't get me wrong. By doing these, you can still have fun and such. You're just being extra careful with who you invest your feelings. At the same time, don't let your memories be filled with just a person or two. Because at one point when they're a step ahead, climbing their way up to the top and leaving you behind (cs that's what life is all about), you'll feel empty.
Anyway, life is all about forgiving but never forget. Don't repeat the same mistake twice!
P/s: But don't take it too seriously, go out and have fun!