Do I need to do a Self Assessment as a landlord?

If you make a profit from rent, almost certainly yes.

You register with HMRC, file a return after the tax year ends, and pay what is owed. The property pages of the return are where rental income and expenses go.

There is a property allowance that covers very small amounts of property income without a return. Above that, register in good time rather than close to the deadline, because getting a Unique Taxpayer Reference takes longer than people expect.