There are a lot of pre-made ones out there, but good on you for having a go yourself.
OK, first thing you need to do is decide on your database tables and fields and how they relate to one another.
Once you have this sorted, go at it to devise your 'add comment' form and then create some queries that INSERT the new comment and SELECT comments to show.
As you will be creating this system yourself, you have all the options open to you, e.g. do you want all comments to be shown without first being approved? Do you give commentators the right to edit their comments? Will you allow then to paste HTML or will you allow BBCode or Markdown? Do commentators need to be logged in or can they just provide an email address and hey presto their gravatar shows?