The conditions for prayer to be valid

Your body must be free of dirt-impurity and you must have wudu (or ghusl if you need one). If there's no water, or using water would hurt you, you do tayammum instead. Praying on purpose without wudu, when you could have made wudu, does not count.

Your clothes must be free of impurity. If you only have enough water to wash either your clothes or your body, wash the clothes and do tayammum for your body. If there's no water at all and most of your clothes are impure, it is better to pray in them (as long as at least a quarter is clean) than to pray with nothing on.

The spot you stand, bow and put your forehead on must be clean: from where your feet stand to where your forehead touches down. If you're on a rug, only that part needs to be clean, not the whole rug. A thick clean cloth can be laid over a dirty spot.

You must cover your awrah, whether you're praying alone or with people around. For a man, that's from the navel to below the knees. For a woman, it's her whole body except her face, hands and feet.

You must face the Qibla (the Kaaba) when you pray. If you're sick, scared of danger, or truly can't work out the direction and nobody can tell you, you pray facing the way you believe is closest and it still counts. But if you never even tried to work it out, it doesn't count, even if you happened to face the right way by luck.

You must make the intention (niyyah), deciding in your heart which prayer you are about to pray, like Fajr or Zuhr, right before or as you start. Saying it out loud is not required, but it's a good habit. The intention must happen before you say the opening Takbir, not after.

The body of the person praying must be free from both physical and ritual impurities. Physical impurity must be removed unless it is below the amount that invalidates prayer, or removing it would mean exposing the private parts in front of others; without wudu, wudu must be performed, and without ghusl where one is needed, ghusl must be performed. If washing with water would be harmful, or no water is available, tayammum should be performed instead. Praying without wudu or ghusl, without a valid excuse, is invalid and intentionally doing so is prohibited.

The clothing of the person praying must be free from physical impurities. If there is only enough water to wash the impure clothing or to perform wudu, but not both, the clothing should be washed and tayammum performed for the prayer. If no water is available and the clothing is entirely or mostly impure (more than three-fourths), the person may pray without clothing or in the impure clothing; it is preferable to pray in the impure clothing if at least a fourth of it is clean, since praying with no clothing at all is not permitted in that case.

The place of prayer, from where the feet are placed to where the head touches in prostration, must be free from impurities.

Covering the awrah is obligatory in prayer, whether alone or in front of others. For men, the awrah is from the navel to below the knees. For a free woman, her entire body is awrah except her face, hands and feet; even hanging hair is awrah by consensus.

Facing the Qibla (the Kaaba) is obligatory. Someone who cannot face it (due to illness, fear of an enemy, or another valid reason) should pray facing whichever direction they are able. Someone unsure of the direction, with no reliable person to ask, should use their best judgement; if they later realise mid-prayer that their judgement was wrong, they must turn immediately, and the prayer is invalid if they delay this for the time it takes to perform one pillar. If they only discover the error after finishing, the prayer need not be repeated. Praying without attempting to determine the direction at all invalidates the prayer, even if it turns out they were facing the right way.

The intention (niyyah) is the firm resolve in the heart to perform the specific prayer (Fajr or Dhuhr, for example) made at the time of starting. Saying it aloud is not obligatory but is recommended, as it aligns heart and tongue; saying it aloud without sincere intention in the heart does not fulfil the requirement. A slip of the tongue (saying "Asr" while intending Dhuhr in the heart) does not matter; the prayer is for what was intended. For fard prayers, specifying which prayer is enough ("Dhuhr"); the date need not be mentioned. For a missed obligatory prayer (qadha), the specific prayer and day must be specified unless only one such prayer is owed. Wajib prayers (such as Eid, or a vowed prayer) likewise need their type specified. Specifying the number of rak'ahs is never required, even if the number intended is mistaken. For nafl, sunnah or Tarawih, intending simply "prayer for Allah" suffices, though specifying is preferred. A follower (muqtadi) must intend to follow the specific imam, except for Jumu'ah, funeral and Eid prayers, which are inherently congregational. The imam needs only to intend to pray, not to intend leading. No specific intention for facing the Qibla is required in any prayer. The intention must be made before the Takbir al-Tahreemah (the opening Takbeer); it is valid slightly before it, provided nothing invalidating (eating, drinking, talking) intervenes, but not after the Takbeer has been said.

The body must be free of both najāsah ḥaqīqiyyah (physical impurity) and ḥadath (ritual impurity). Physical impurity must be removed unless it falls below the threshold that invalidates prayer, or its removal would require exposing the ʿawrah before others; ritual impurity is removed by wuḍūʾ, or ghusl where a major impurity (janābah, ḥayḍ, nifās) is present. Where water would be harmful or is unavailable, tayammum is substituted. Praying without wuḍūʾ or ghusl, absent a valid excuse, is invalid, and deliberately doing so is ḥarām.

The garments worn in prayer must be free of najāsah. Where water suffices only for washing the impure garment or for wuḍūʾ, but not both, the garment is washed and tayammum performed. Where no water is available and the garment is wholly or mostly (more than three-quarters) impure, the muṣallī may choose between praying unclothed or in the impure garment; praying in it is preferred where at least a quarter remains clean, since praying with nothing to cover the ʿawrah is not permitted in that circumstance.

The makān, from the point where the feet stand to the point where the forehead touches in sujūd, must be free of najāsah.

Covering the ʿawrah is obligatory whether one prays alone or before others. For a man the ʿawrah extends from the navel to below the knee. For a free woman the whole body is ʿawrah excepting the face, the hands (to the wrist) and the feet; loose, hanging hair is ʿawrah by consensus (ijmāʿ) of the school.

Facing the qiblah (the Kaʿbah) is obligatory. It is waived for one unable to face it through illness, fear of an enemy, or another valid excuse, who then prays toward whichever direction he is able. One uncertain of the direction, with no reliable informant available, must exercise ijtihād; discovering the error mid-prayer obliges an immediate correction, failing which, if the delay extends to the length of one rukn, the prayer is invalidated. Discovering the error only after completion does not require repetition, since the ijtihād was validly exercised at the time. Praying without any attempt at ijtihād invalidates the prayer even where the qiblah was, by chance, correctly faced, since the condition is the exercise of due diligence, not merely the outcome.

The niyyah is the resolve of the heart to perform a specified prayer (Fajr or Ẓuhr, for example) formed at the commencement of the prayer. Verbal expression (talaffuẓ) is sunnah, not a condition, and serves only to bring the tongue into agreement with the heart; utterance without corresponding intent in the heart does not suffice. An error of the tongue that contradicts the heart's intent (saying "ʿAṣr" while intending Ẓuhr) is immaterial. For farḍ prayers, naming the prayer suffices without specifying the day; for qaḍāʾ of a missed farḍ, both the prayer and the day owed must be specified unless only a single instance of that prayer is owed. Wajib prayers require the specific type to be intended, including which ʿĪd, and the specific type of sajdah where relevant. The rakʿah-count need never be specified, and an erroneous count intended does not affect validity. For nafl, sunnah or tarāwīḥ, a general intention ("prayer for Allah") suffices, specificity being merely preferable. A muqtadī must intend to follow the particular imam, except in Jumuʿah, funeral and ʿĪd prayers, which are congregational by their nature. The imam requires no intention of imāmah as such, intending the prayer itself suffices, save that where a woman is to follow him, he must specifically intend to lead her, or her following is not valid (though his own prayer is unaffected). No intention regarding the qiblah is required in any prayer, farḍ, wājib, sunnah or nafl. The niyyah must precede or coincide with the takbīrat al-taḥrīmah; forming it slightly before the takbīr is valid provided nothing that would invalidate the prayer (eating, drinking, speaking) intervenes between the two, but forming it after the takbīr has been pronounced is not valid.