How to address a Judge?

It will depend on which country you're in. Sounds like you're in a local court; most likely dealing with a magistrate. District Court is for things like murder or GTA. "Your Honour" is the safest bet. "My Lord" is only appropriate in higher English courts; "Your Worship" is outmoded everywhere but South Africa. If you are a lawyer, then "sir" is unlikely to be acceptable when addressing any judge outside of the UK. Isn't common law fun? 

Address the judge directly as: "My Lord" or "My Lady" or indirectly as "Your Lordship" or "Your Ladyship". 

When referring to real judges by name make sure you get their names correct. Smith J. in speech is: "Mr Justice Smith" or, if a woman, "Mrs Justice Smith". In speech "Smith J." or "Justice Smith" is wrong.

If you know the name of the judge to whom you are writing, then you would address it to "Mr Justice ***" and the greeting on the letter would be "My Lord"

This link is very comprehensive on the matter:
http://www.judiciary.gov.uk/about_judiciary/forms_of_address/index.htm

Good luck!

High Court/court of appeal/house of lords - my lord / my lady (your lordship for you)

crown court - your honour

circuit judges - sir or madam

magistrates - your worship or sir/madam

tribunal chairman - sir or madam

master of the high court - master

 Depends on which court you are being tried in.