Rebuilding trust after an affair is a process. Both spouses play a part in this. For the spouse who had the affair, the burden is heavy. It is their role to be honest, truthful, and faithful. They have to provide the foundation that is consistent enough to rebuild trust. It is a very difficult and sometimes frustrating process because they are waiting for their spouse to respond - to believe that the changes are real and that does not come easy.
As the offending spouse works on changes that will rebuilt trust, it is the role of the other spouse to begin to accept the changes. This can be very difficult and usually happens in baby steps. The spouse that has been hurt will do everything they can do to keep from being hurt again. It is a long process.
It is sometimes helpful for the spouse that had the affair to ask the other spouse what they can do to rebuild the trust. This gives specific things to work on. It also lets the offending spouse know the things that are important to do.
Bottom line: It will take time, perseverance, and consistency. There is not a shortcut.