One thing that I enjoy doing in Vatican City is attending Mass, especially on special days like Palm Sunday.   St. Peter's Square can take on a "rock concert" atmosphere with pilgrims excitedly and energetically participating.   However, on Sunday and other Catholic holidays, the Vatican Museums are closed.

Also, abbreviated wear (short skirts, uncovered shoulders, short shorts, etc.) is not permitted and visitors will be denied entry if your outfit is deemed inappropriate, no matter how long you have waited in line.

I think Vatican City is most crowded on Mondays since many other attractions in Rome are closed on Mondays.   Don't try to outsmart the crowds by getting there early during the week - everyone else is thinking just like you.   I find the best time to avoid lines is by visiting later in the afternoon.

For a tour of the Vatican, you can just show up, pray for a short line (not likely) and do the tour.   However, the smart way to do it is to schedule a guided tour.  There won't be any waiting in line and the guides will fully explain what you are looking at.  On our small group tours to Italy, we only do guided tours of the Vatican Museums (including the Sistine Chapel).   To reserve a tour, see the official Vatican website:  http://mv.vatican.va/3_EN/pages/z-Info/MV_Info_Servizi_Visite.html

Another tip is to visit the Vatican Museums and Sistine Chapel when they are open on Friday evenings in late summer/early fall.  Visitors can practically have the place to themselves.

For more information on my small group tours to Italy, see www.travelingprofessor.com or my FB page:  https://www.facebook.com/pages/The-Traveling-Professor/136094362898