The Speaker can allow any MP to make a personal statement. They are usually related to conduct. For example, if the Standards Committee recommends that an MP make a personal statement for having breached the Code of Conduct, the Speaker will generally allow this.
If the Speaker has agreed that you can make a personal statement, the text must be cleared with the Speaker in advance, and must not be altered. Members making a statement on the circumstances of their resignation from the Government do not need the Speaker's permission or to clear the text.
Personal statements are made after Question Time and any urgent questions or oral statements.
The annunciators (the monitors around the parliamentary estate) will show that a personal statement is taking place.
Personal statements are heard without interruption, there are no questions, and the Speaker does not take points of order on them.