When can I consider my menstruation (Hayd) to be over?

There are two signs that indicate the end of menstruation:

1. The appearance of a white discharge (al-Qassa al-Baydaa) at the end of the period.
2. Complete cessation of menstrual bleeding, confirmed by inserting a piece of cotton or similar material and finding it clean without blood or yellowish-brown discharge.

Some women rely on the white discharge, others only rely on dryness. This white discharge is a different sign from the discharge that can increase in the days before a period even starts; see why discharge increases before your period for that earlier, unrelated change. Light spotting that shows up before a period starts is a separate question again, not this end-of-period sign; see why you might notice spotting before your period for what that is instead.

If menstrual bleeding stops and the area is dry and completely free of blood, your menses have ended and you are pure. You should not pay attention to subsequent yellowish or brownish discharge, based on the hadith of Umm ‘Atiyyah: “We used not to regard the brownish or yellowish discharge after the Tuhr as being of any significance.” (Narrated by al-Bukhari). Once you have identified tuhr, ghusl is what restores your purity for prayer, covering the steps and the hadith they rest on. For fasting specifically, what decides that day's fast is whether tuhr arrived before or after Fajr, not when ghusl itself follows it. If purity arrives while you are travelling and there is no water available for Ghusl, see what if your period starts while you're travelling for how tayammum applies until you can reach it. A period tracker for Muslim women that lets you log which of these two signs you actually saw, rather than just a date, makes this distinction easier to catch each month.