The first Azed puzzle of each month is linked to a clue writing competition, with the entries being sent directly to, and judged by, Azed; he accepts emailed entries from overseas solvers, though not from solvers in the UK.
For all other Azed puzzles the prizes are awarded on a 'picked at random' basis by the Guardian, and they accept entries only by post.
I hope that you are enjoying the puzzles, as Azed is a master of his craft.