You are probably devastated after finding out your girlfriend lied and cheated. You may never want to look at or speak to her again. You may also realise how much you care for her and do not want to lose her. These are all normal feelings after a betrayal and will not go away overnight. If you truly love your girlfriend, make an effort to get past the pain you feel. Your relationship going forward may turn out to be even more rewarding.
Ask your girlfriend for space. Tell her you need to be alone for a while. You may need a week or more until you are ready to confront her. Take this time to calm your emotions so that you don't yell at your girlfriend and possibly say something in anger that could ruin all chances of a reconciliation. You also need to think long and hard about whether you want to make the effort to salvage your relationship. If your girlfriend cares about your feelings, she will give you the time you need.
Find out if your girlfriend truly wants this relationship with you. Sit down and have a heart-to-heart talk with her. You need complete honesty at this point. Don't be afraid to come right out and ask if she wants you. You need to know if you are both on the same page so that you can move forward.
Find out the reasons for the lying and cheating. You may hear things that you don't want to know, such as you have been busy and never have time for her. It may hurt, but you may have to accept that you have not been the perfect boyfriend. This open conversation gives you a chance to work on areas to improve your relationship going forward.
Lay down the ground rules so that you don't get hurt again. Explain that you need complete honesty going forward. Tell her if she cheats again, the relationship is over. You deserve to be treated with respect just as does she.
Get support from friends and family when you need it. Call a friend and tell him you need to vent for a few minutes. Alternatively, go to a movie with a friend or family member to get your mind off your troubles.
Seek counselling together. You may need extra help to get the relationship on track. Counselling may be the best option during this difficult time. You may also want to speak to a trusted spiritual adviser.
You may have to end the relationship if your girlfriend does not take responsibility and does not give you the time to fully recover. However, this is only something that you can decide. No one else can tell you what is best for your life.