Who has to file, and when?
Anyone with income that is not taxed at source: sole traders, partners, landlords, company directors taking dividends, and employees with significant untaxed income or a high enough salary to trigger it. HMRC's checker on gov.uk gives a definitive answer for an individual case.
The return covers the tax year, 6 April to 5 April. Online returns are due by 31 January following the end of the tax year, paper returns by 31 October. The tax is also due on 31 January, along with any first payment on account for the year already under way.
The name is literal: you assess yourself. HMRC does not check every figure when the return is filed; it accepts it, and reserves the right to enquire later. That is why the records behind the return matter more than the return itself.