Firstly a warning: Don't hold your breath on getting in.
Secondly (and arguably more helpfully):
The letter should be no more than a page long (half a page is probably adequate).
Snail mail or email is fine - why not do both (possibly add to the email: "a hard copy is in the post I sent this to ensure I made the jan4th deadline").
The letter should include a rundown on why you should be let in to ----/Law. These fall in two categories; why you are good (eg did well in legal studies, school debated, etc) and why you didn't get a good enough UAI (eg how you have been disadvantaged).
As far as whom to send it to I believe the UAC guide directs you to send it to student admin (who will then send it to the relevant faculty).
Attatch any and all supporting documentation you can muster eg school reference, maybe a personal reference from a teacher, official recognition of your disadvanatge, etc.
Try and make the jan4th deadline - shell out for next day express.
Follow the letter up with a personal visit - around say the tenth- drop in at student admin (pauline griffith building) and get directions to see the relevent people. Plead in person, make a good impression.
Do all these things and you might get lucky. However be warned that in a high demand course like Law there may simply be not enough room eg Arts last year was only accepting these 'special consideration' cases where the person was eligible for entry under EAS etc but had for some reason not applied under EAS. This was <5 people.
Consider just doing ----- and then transferring into -----/Law.
