The core elements of ablution are given in the Qur'an in Al-Mā'idah 5:6:
"…When you rise for prayer, wash your faces and your hands up to the elbows, wipe your heads and (wash) your feet up to the ankles…" (5:6)
When water is unavailable — tayammum: 5:6 and An-Nisā' 4:43 prescribe wiping the face and hands with clean earth.
Source: Qur'anic verses (M. Okuyan meal).
يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَقْرَبُوا۟ ٱلصَّلَوٰةَ وَأَنتُمْ سُكَـٰرَىٰ حَتَّىٰ تَعْلَمُوا۟ مَا تَقُولُونَ وَلَا جُنُبًا إِلَّا عَابِرِى سَبِيلٍ حَتَّىٰ تَغْتَسِلُوا۟ ۚ وَإِن كُنتُم مَّرْضَىٰٓ أَوْ عَلَىٰ سَفَرٍ أَوْ جَآءَ أَحَدٌ مِّنكُم مِّنَ ٱلْغَآئِطِ أَوْ لَـٰمَسْتُمُ ٱلنِّسَآءَ فَلَمْ تَجِدُوا۟ مَآءً فَتَيَمَّمُوا۟ صَعِيدًا طَيِّبًا فَٱمْسَحُوا۟ بِوُجُوهِكُمْ وَأَيْدِيكُمْ ۗ إِنَّ ٱللَّهَ كَانَ عَفُوًّا غَفُورًا
O ye who believe! Draw not near unto prayer when ye are drunken, till ye know that which ye utter, nor when ye are polluted, save when journeying upon the road, till ye have bathed. And if ye be ill, or on a journey, or one of you cometh from the closet, or ye have touched women, and ye find not water, then go to high clean soil and rub your faces and your hands (therewith). Lo! Allah is Benign, Forgiving.
يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا قُمْتُمْ إِلَى ٱلصَّلَوٰةِ فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ وَٱمْسَحُوا۟ بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى ٱلْكَعْبَيْنِ ۚ وَإِن كُنتُمْ جُنُبًا فَٱطَّهَّرُوا۟ ۚ وَإِن كُنتُم مَّرْضَىٰٓ أَوْ عَلَىٰ سَفَرٍ أَوْ جَآءَ أَحَدٌ مِّنكُم مِّنَ ٱلْغَآئِطِ أَوْ لَـٰمَسْتُمُ ٱلنِّسَآءَ فَلَمْ تَجِدُوا۟ مَآءً فَتَيَمَّمُوا۟ صَعِيدًا طَيِّبًا فَٱمْسَحُوا۟ بِوُجُوهِكُمْ وَأَيْدِيكُم مِّنْهُ ۚ مَا يُرِيدُ ٱللَّهُ لِيَجْعَلَ عَلَيْكُم مِّنْ حَرَجٍ وَلَـٰكِن يُرِيدُ لِيُطَهِّرَكُمْ وَلِيُتِمَّ نِعْمَتَهُۥ عَلَيْكُمْ لَعَلَّكُمْ تَشْكُرُونَ
O ye who believe! When ye rise up for prayer, wash you faces, and your hands up to the elbows, and lightly rub your heads and (wash) your feet up to the ankles. And if ye are unclean, purify yourselves. And if ye are sick or on a journey, or one of you cometh from the closet, or ye have had contact with women, and ye find not water, then go to clean, high ground and rub your faces and your hands with some of it. Allah would not place a burden on you, but He would purify you and would perfect His grace upon you, that ye may give thanks.