Dress requirements for prayer
What is to be covered?
For prayer to be valid the private areas must be covered with a loose garment so as not to show the privates. Therefore, a man should be covered loosely from the shoulders to the knees. It is prohibited for the lower garment to hang past the ankles, even when not praying. A woman should loosely cover herself completely from head to toe except her face. It is better that she covers her hands with gloves or clothe.  The top of her feet must be covered either with a long dress, socks or whatever. She must cover the top of her feet otherwise her prayer will not be accepted. If there are non- mahram men around, the face must be covered.
The prayer is not valid unless the "private area" is covered, which for the prayer of the adult, free woman implies everything but her face. She is not required to cover her face during the prayer unless there are non-related (i.e. non-mahram) men around her. She must then cover her face except to her husband and her male relatives [within the prohibited degrees of marriage, see An-Nur 24:31]
"O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes of one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed  (Al-Ahzab 33:59) 
As for the face, it is Sunnah for her to uncover it during the prayer if there are no non-related men around her. As for the feet, it is obligatory upon her to cover them according to the majority of the scholars. Some scholars allow the feet to be uncovered but the majority say it is prohibited to uncover them and she must cover them. Abu Dawud recorded that Umm Salama (RA) was asked about a woman praying in a headcovering and long gown and she said, "There is no harm in that as long as the gown covers the top of her feet." So covering the feet is better and safest under all circumstances. As for the hands, their situation is simpler. If she uncovers them, there is no harm. If she covers them, there is no harm. Some scholars say it is better to cover them. And from Allah comes guidance to the correct path. - Shaikh ibn Baz (rahmatullahi alay)
"And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc.) and not to show off their adornment except only that which is apparent (like palms of hands or one eye or both eyes for necessity to see the way, or outer dress like veil, gloves, head-cover, apron, etc.), and draw their veils all over Juyubihinna (i.e. their bodies, faces, necks and bosoms, etc.) and not to reveal their adornment except to their husbands, their fathers, their husband?s fathers, their sons, their husband?s sons, their brothers or their brother?s sons, or their sister?s sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or small children who have no sense of the shame of sex. And let them not strike  their feet so as to reveal  what they hide of their adornment?: (An-Nur 24:31) 
Hadeeth that support the matter
The Prophet (SAW) said, "The Salat of a woman, who has reached puberty, is not accepted unless she is wearing a Khimar." (Sahih -Al-Khamsa except An-Nasaa?ee) 
Aisha (RA) used to say: "When the Verse: "They should cover (draw their veils over) their bodies, faces, necks, and bosoms etc.
(An-Nur 24:31) was revealed, (the ladies) cut their waist sheets at the edges and covered their  faces with those cut pieces of cloth (sahih Bukhari)
regarding men wearing long garments:
The Prophet (SAW) said, "The part of an Izar (lower-half body cover) which hangs below the ankles is in the Fire." (Sahih - Al-Bukhari)
Prophet Muhammad (SAW) used to say: "All actions are by intentions, and every man shall have what he intended." ( Sahih - Al-Bukhari, Muslim )
note: A Khimar is a piece of cloth with which a woman covers her head and neck area. It means that the whole body of a woman should be loosely covered including head hair. - Bulugh Al-Maram
Narrated Umm Salama (RA): She asked the Prophet (SAW), "Can a woman pray in a long dress and veil  wearing a lower garment?" He (SAW) replied, "If the long dress is ample and covers the surface of her feet." (Mawquf - Abu Dawud)
"Seeking Knowledge is a duty on EVERY Muslim" (Bukhari)
     Locating and Facing the Qiblah   
                (prayer direction)
Wherever a person is in the world, they should face towards the Ka'bah when they are going to pray. The Ka'bah is the sacred mosque in Makkah, Saudi Arabia. Facing towards the Qiblah is a very important condition in the performance of prayer. However, if the person is in a place such as a desert, jungle, unknown strange city or a place where he/she does not know the direction of the Qiblah, they should try their best to find out the direction of the Qiblah from others. However, if it is not possible then they should use their best judgment and face in a direction which they think is that of the Qiblah and Allah (SWT) will accept his prayer, Insha-Allah.
IIt is important to start the prayer facing the direction of the Qiblah and it does not matter if his direction changes while he is praying (i.e. in a ship, a train, or an airplane, etc.).
Allah (SWT) said, "...Surely, We shall turn you to a Qiblah (prayer direction) that shall please you, so turn your face in the direction of Al-Masjid-al-Haram (at Makkah). And wheresoever you people are, turn your faces (in prayer) in that direction..." (Al-Baqarah 2:144)
the prophet (saaws)said, "When you stand for prayer, perform wudu perfectly, then face the Qiblah and say takbir. (sahih Bukhari)
     On the Ground, and on Mats
If the ground is not too hot, dirty or hard, there is no need for a mat when praying. Prostrating on the bare ground is the best prostration.
"His (SAW) Companions (RU) would pray with him in the intense heat, so when one of them could not press his forehead against the ground, he would spread his robe and prostrate on that." (Sahih - Muslim)
         Establishing a  Sutrah
Place tall anything just beyond the place of prostration. Things that can be used are: a wall, bed, tall pillow, tall diaper bag, tall purse, tall stick, tree, etc. Anything that breaks the path between the person praying and someone who "may" need to pass in front. It's best to pray facing a wall, bed, or any other type of tall object, so that there will be no need for someone to pass directly in front. Do not mind anyone who passes beyond the sutrah. The Prophet (SAW) said, "Do not pray except towards a sutrah, and do not let anyone pass in front of you, but if someone continues (to try to pass) then fight him, for he has a companion (i.e. a Shaitan) with him." (Sahih - Al-Bukhari and Ahmad) 
"When he (SAW) prayed (in an open space where there was nothing to use as a sutrah) he would plant a spear in the ground in front of him and pray towards it with the people behind him." (Sahih - Al-Bukhari and Muslim) 
The Prophet (SAW) said, "When one of you places in front of him something such as the stick on the end of a saddle, he should pray and not mind anyone who passes beyond it." (Sahih - Muslim and Abu Dawood)