Entering the mosque when the imam is standing

Whoever enters the mosque
when the imam is reciting al-Faatihah should say the opening takbeer, then
be silent until the imam has finished reciting al-Faatihah, because the
person who is praying behind an imam is enjoined to listen attentively to
the recitation of his imam, and his reciting the opening du’aa’ and seeking
refuge with Allaah will distract him from listening attentively as he is
enjoined to do. He should not let himself be distracted from that which he
is enjoined to do. 

See Majmoo’ al-Fataawa, 23/280 

His view – that he should not recite the opening du’aa’ or
seek refuge when his imam is reciting out loud – is the more correct of the
two scholarly views on this matter, in sha Allah. It is the view favoured by
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) as stated in
Majmoo’ al-Fataawa (22/341 and 23/271), because of the strength of the
evidence. The Prophet (peace and blessings of Allaah be upon him) said:
“The imam has been appointed to be followed, so when he says takbeer, then
say takbeer, and when he recites, listen attentively.” Narrated by Muslim,
404; al-Nasaa’i, 921. 

When the imam has finished al-Faatihah, the person behind him
may say the opening du’aa’, then pray for refuge with Allaah and recite the
Basmalah and al-Faatihah. If he cannot recite the opening du’aa’ and prayer
for refuge and recite before the imam starts to recite the next soorah, then
he should not recite the opening du’aa’, because the opening du’aa’ is
Sunnah; rather he should recite the prayer for refuge and al-Faatihah,
because the Prophet (peace and blessings of Allaah be upon him) said
with regard to reciting behind the imam: “Do not do anything but recite the
Essence of the Qur’aan [al-Faatihah], for there is no prayer for the one who
does not recite it.” Narrated by al-Tirmidhi, 311; classed as saheeh by
al-Albaani in Saheeh al-Tirmidhi. 

This is according to the
view that it is obligatory for the person who is praying behind an imam in a
prayer where Qur’aan is recited out loud to recite al-Faatihah. The correct
view is that it is obligatory for him, because of the general meaning of the
words of the Prophet (peace and blessings of Allaah be upon him):
“There is no prayer for the one who does not recite the Opening of the
Book.” Narrated by al-Bukhaari, 756. This means that such a prayer is not
valid. 

See also question no. 10995 

But if he enters the mosque and the imam is offering a prayer
when Qur’aan is recited silently, then he should say the opening takbeer and
recite the opening du’aa’ and prayer for refuge, then recite al-Faatihah if
he thinks that he can complete it before the imam bows, so that he may earn
the reward for reciting the opening du’aa’ and al-Faatihah. Otherwise he
should focus on al-Faatihah after saying the opening Takbeer, and not recite
the opening du’aa’, because it is more important to pay attention to that
which is obligatory. 

See Mughni al-Muhtaaj, 1/257; Talbees Iblees,
p. 161 

If the imam bows, the
person praying behind him should leave the rest of al-Faatihah and bow with
him, because he has only caught up with what he has recited, and he has
caught up with the rak’ah, as is the case if he catches up with him when he
is bowing. So in this case the obligation to recite al-Faatihah is waived,
and he should not lag behind his imam in order to complete al-Faatihah,
because the Prophet (peace and blessings of Allaah be upon him) said:
“When he bows, then bow.” Narrated by al-Bukhaari, 378; Muslim, 414. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: 

Reciting the opening du’aa’ is Sunnah
and reciting al-Faatihah is obligatory for the one who is praying behind an
imam, according to the correct scholarly opinion. If you fear that you will
miss al-Faatihah, then start with it, and if the imam bows before you have
completed it, then bow with him and the rest of it is waived in your case,
because the Prophet (peace and blessings of Allaah be upon him) said:
“The imam has been appointed to be followed, so do not differ from him. When
he says takbeer, then say takbeer; when he bows, then bow…” Agreed upon. End
quote. 

Majmoo’ Fataawa Ibn Baaz,
11/243-244. 

And Allaah knows best. 

See Ahkaam Hudoor al-Masaajid, p. 139-141, by Shaykh ‘Abd-Allaah ibn Saalih al-Fawzaan.