“Call on your Lord humbly and secretly; surely He does not love those who exceed the limits.”
This is the same as the Christian Bible's instructions to pray in private, as Jesus did. It seems that the monotheistic God - being omniscient (all-knowing) - does not require or endorse mass displays of piety, which too easily become bombastic public dramas rather than genuinely-felt acts.
The Qur'an says little else on how to pray. Although some prayers, daily routines and the like are hinted at, there are few specifics. Just before praying, Qur'an 3:191 mentions that those who remember Allah' while 'standing, sitting, and laying down' (some translations say 'laying down on their side') are 'men of sense'. It doesn't here mention women who pray. This gives a lot of options as to posture! An example prayer is then given in Qur'an 3:191-194:
Our Lord! You have not created this without purpose, glory to You! Give us salvation from the torment of the Fire.
Our Lord! Verily, whom You admit to the Fire, indeed, You have disgraced him; and never will the Zalimun [polytheists and wrong-doers] find any helpers.
Our Lord! Verily, we have heard the call of one calling to Faith: 'Believe in your Lord,' and we have believed. Our Lord! Forgive us our sins and expiate from us our evil deeds, and make us die (in the state of righteousness) along with Al-Abrar [the pious believers of Islamic Monotheism].
Our Lord! Grant us what You promised unto us through Your Messengers and disgrace us not on the Day of Resurrection, for You never break your Promise.
Some say that Qur'an 3:43 gives instruction to bow down. But this is clearly just part of a sentence being addressed to Mary, "Mary, be obedient to your Lord; bow down and worship with the worshippers", or in most translations "with those who bow down". Although according to Qur'an 3:191 they could be standing, sitting or laying. If Mary represents women in general, Qur'an 3:43 at most instructs women to bow down with worshippers. Yet, against the Qur'an, many Islamic institutions separate women from men rather than have them pray with them.
Just to add to the confusion, don't forget that Qur'an 7:55 instructs believers to pray humbly and in secret/private. So perhaps women - and men - shouldn't bow down with anyone and Qur'an 3:43 does indeed apply only to Mary. What you do depends on which verses you choose to follow.
Qur'an 52:48-49 hints at some timings, "Give glory to your Lord when you awaken, in the night-time praise Him, and at the setting of the stars" (Dawood translation). Or: "So wait patiently (O Muhammad) for thy Lord's decree, for surely thou art in Our sight; and hymn the praise of thy Lord when thou uprisest, And in the night-time also hymn His praise, and at the setting of the stars" (Muhammad Pickthal translation). This has various interpretations as to when you should pray:
Qur'an 73 opens with commentary that the recital of the Qur'an is to be a chant. And, at night-time voice impressions are strongest and more eloquent than during the day, when daytime business distracts people (Qur'an 73:1-7). Although, Qur'an 73 may well be addressed solely to Muhammad, as it warns "We are about to address to you words..." (73:5), so it may just be night-time was the best time for the angels to address Muhammad, the Qur'an is nonetheless asserting the general principal that, despite tiredness and the like, night-time is a clearer time to chant the Qur'an. Or perhaps, Muhammad was an epileptic (or he suffered from a form of sleep apnea), and had more frequent visions at night-time, hence, the belief and assertion that the night-time was the best time for receiving and reciting the Qur'an.
For comparison to Christianity and for notes on prayer across all religions, see: