Don't be fooled by the term. Most Quaker Meetings will meet weekly and the "Monthly Meeting is a reference to the practice of Meeting for worship in Business that takes place after the weekly Meeting once a month; it is the Quaker term for "local congregation."
In the "unprogrammed Meetings" (programmed Meetings are usually Evangelical Quakers and hard to tell from say Methodists) you would go into the Meeting room at the appropriate time or just before, find a seat and "center down" or consider the purpose of your presence in anticipating the presence of the Spirit with possible leadings from it. The entire Meeting might be silent, or some of the members might feel led to give a message to the group. As a rule, any such ministry would be quietly respected and absorbed rather than responded to immediately. Part of the silence would be discerning whether any "leadings" felt were for you as an individual or meant to share. At the end of the time for "silent worship" a member might stand and signify that the silent meeting is over as led and then usually announcements of general interest would be made and visitors asked if they would like to identify or say something about themselves....no pressure. After that, general fellowship and/or who knows what.
I hope that helps.
