Be in a good state
It is recommended to be clean and calm, in a quiet place, and to face the qibla if you can. Many people also clean their mouth and wear clean clothes.
The four schools agree that a person without wudu (ablution) may recite from memory. Most scholars say that you should have wudu to touch the mushaf (the printed Quran), based on the verse "none touch it except the purified" (Quran 56:79), while a minority of scholars allow touching it without wudu. Contemporary scholars differ on a phone or tablet screen, and many allow it.
Scholars also differ about reciting in a state of major impurity. The Hanafi, Shafi'i and Hanbali schools say that a person who needs a ghusl (full bath) should wait until after it, while the Maliki school allows a small amount, and some scholars allow more. For a woman in her monthly period, the Maliki school allows recitation, while most scholars of the other schools say that she should not recite the Quran. Many contemporary scholars allow her to recite when she needs to, for example when teaching, studying or protecting what she has memorised. A woman may always make dhikr and dua. If you have a question about your own case, ask a qualified local scholar.
Be kind to the Quran in simple ways. Keep the mushaf in a clean, high place, and do not put things on top of it. When you finish a session, close it with care.