How does one participate in the 5 daily prayers in congregation?
I know how to pray all of the 5 Prayers. All I require is knowledge of the do's and don'ts.
In that case all you may have to do is:
Pray tahiyat al masjid (salutation of the mosque) once you enter the mosque if you reached it before the congregation prayer starts. It's a nafl of two rak'a.
Note that I'm assuming you are a male, as for female jahr is not allowed at all!
Once the congregation has started you should follow the Imam and never be ahead of him in any act.
You should never recite Quran behind the Imam (at least not loudly).
In siri prayers like dohr, 'asr and the last rak'a of maghrib or the two last rak'as of 'isha' you should recite al-fatiha in low voice or for yourself.
I think my answers for
What are the rules for reading 4 rak'a fard with jamat or alone?,
Do we have to say 'Allahu Akbar' loudly in every rakat of every salat?,
Struggle to keep up with the Imam during prayer at the mosque,
How can we offer Fard Namaz with just two people
clearly show how to do it and have enough evidences, .
Now if the Imam finished in a jahri prayer reciting al-fatiha you should say or respond "ameen", when he says -in any prayer- after ruku': sami'a Allahu liman hamidah, you should answer: Rabana walaka-l-hamd ... (for yourself->low voice).
If you are hanafi and the Imam also you should do taslim following him if not I'm personally waiting until he finishes the 2nd tasleem as I don't see any evidenced reason for the pause he does between both tasleems.
Now if you reached the mosque and the prayer has already started you may need to follow this hadith and see this post What is the exact manner to join the Salat Jamat after arriving late? for details.
Note that Friday prayer is a 2 rak'a prayer which only starts after the two Khotbas of the Imam (a speech or sermon) and is held loudly (as a jahri prayer).
I hope this may help you for your visit at a mosque.