Niyyat (intention) is the action of the heart. You just have to intend in your heart to perform the prayer.
The Five Daily Prayers
For any of the five daily prayers, it is obligatory to intend a minimum of three things:
That one is praying; That this prayer is an obligation (Ar. fard); The specific prayer; e.g. fajr. For example, one would intend to pray the fard of fajr when praying it. The analogous intention has to be present for the other four prayers. These components of the intention have to be there whether the prayer is offered alone or in a group.
As for the timing of the intention, it should occur while saying Allahu Akbar. This simply means that while saying Allahu Akbar you should be conscious that you are praying fajr and that it is an obligation. You would substitute the actual prayer you are offering in place of fajr for the other prayers.
What About Intending Praying in Congregation?
A follower must intend congregation before following the imam’s movements. A follower intends following the imam (Ar. iqtida’) while the imam intends being an imam (Ar. imamah). It is also valid for either (or both) to intend congregation (Ar. jama’ah). Only after this intention is made does one start to get the reward of praying in congregation. Therefore, it’s ideal to make this intention during the opening Allahu Akbar along with the other components of the intention. If the imam forgets to intend the congregation for dhuhr and only does so in the second rak’ah, he gets the reward of praying three rak’ahs in congregation and one rak’ah alone. If the imam never intends congregation, he gets the reward of praying alone. Those who made the intention of following him get the reward of praying in congregation.
The Friday Prayer
Unlike the five daily prayers, it is not valid to offer the Friday prayer alone. Therefore, when offering the Friday prayer, one must intend four things:
That one is praying;
That this prayer is an obligation (Ar. fard);
That it is the Friday prayer;
That it is in congregation. (Alternatively, the imam can intend being an imam and the follower can intend being a follower.)
All four components must be present during the opening Allahu Akbar of the Friday prayer. So while saying Allahu Akbar you should be conscious that you are praying the obligatory Friday prayer in a group.
Allah the Exalted knows best.
Niyyah (intention) is actually from the heart. It is not necessary to make a verbal intention before performing Salaat. However, if a person is in doubt and the verbal intention helps one to strengthen the intention in the heart, then one may make verbal intention before Salaat.
One should not regard verbal intention as necessary and a precondition for the validity of Salaat.
and Allah Ta'ala Knows Best
Mufti Ebrahim Desai
Regarding Salat At-Tasbeeh, please see: http://www.shafiifiqh.com/salat-al-tasbih/
For the Shafi'i madhhab,
I'd also like to know when praying behind an imam, what are we supposed to recite when a surah is being recited like during a tarawee prayer or even a regular five time prayer?
As for one following an imam, he may be in one of two situations:
1) He is able to hear the imam‘s recitation, like when the prayer is audible, such as: subh, maghrib, and ‘isha.
2) He is unable to hear the imam‘s recitation, such as when the prayer is inaudible or one is unable to hear the imam’s recitation.
In the first situation, it is not recommended that a follower recite a surah, as our School considers it to be disliked. The follower (after reciting the Fatihah) should instead, listen attentively to the imam‘s recitation, taking heed to Allah’s injunction, “when the Quran is recited, listen closely to it.” (Surat al-’Araf 204)
In instances where one is unable to hear the imam‘s recitation, the follower is recommended to recite a surah after the Fatihah according to what is relied-upon (ar: al-asahh).
Not being able to hear the imam‘s recitation can be for a number of reasons, including: the prayer being inaudible (like as zuhr and asr), being far from the imam, being able to hear theimam‘s voice but unable to comprehend what he is reciting, etc.
Consequently, it is recommended for the follower to recite a surah after the Fatihah in inaudible prayers. Likewise, the follower may recite a surah in prayers that are normally audible, but due to being far from the imam one is unable hear his recition or when one can hear but is unable to make out what is being recited.
And, Allah knows best
Sidi Mahmud Adams
And for the Hanafi people,
The Muqtadi (follower) Should Listen and Remain Silent.
However, if a person did recite behind the Imam, Salah will be complete.