How do I pray behind an imam?

The basic rule: follow, don't race

The Prophet ﷺ said that the imam is there to be followed: when he says "Allahu akbar", say it; when he bows, bow; when he says "Sami'allahu liman hamidah", say "Rabbana wa lakal-hamd"; and when he prostrates, prostrate (Sahih al-Bukhari 722). So your movements come right after his, not at the same moment and not ahead of him.

Going down or coming up before the imam is a serious mistake. The Prophet ﷺ warned the person who raises his head before the imam that Allah could turn his head into the head of a donkey (Sahih al-Bukhari 691). The point is simple: in congregation you are one body moving together, and the imam sets the pace.

Step by step

• Intention: in your heart, intend to pray this prayer behind the imam. No words are needed.
• Join the row: fill the front rows first and stand close to the people next to you.
• Opening takbir: say "Allahu akbar" after the imam finishes his.
• Movements: bow, rise, prostrate and sit after him, listening for his "Allahu akbar".
• Ameen: in loud prayers, say "Ameen" after he finishes al-Fatiha (Sahih al-Bukhari 780).
• Ending: give your salam after his. If you joined late, stand up and finish what you missed.

If you still need the basics of each position, see How do I pray as a Muslim?

Do I recite al-Fatiha behind the imam?

Scholars differ here. The Hanafi school says the follower stays silent, because the imam's recitation counts for him. The Shafi'i school says the follower recites al-Fatiha in every unit, quietly. Malikis and Hanbalis generally say listen in the loud prayers (Fajr, Maghrib, Isha) and recite in the silent ones. All of these are respected positions, so follow what your local mosque or teacher follows. See Why is Surah al-Fatiha in every prayer?

Mistakes new Muslims worry about

If you lose track and do something a moment late, just catch up; that is forgiven. If you forget something small, the imam's prayer covers most minor slips of the follower. And if you can't hear well, watch the person beside you. Nobody expects perfection on your first visit. See Can I pray with Muslims if I'm not Muslim yet?