This may sound like a stupid question, but how do I transfer my Pokémon and items from the Omega Ruby/Alpha Sapphire demo to the full game?

Start the demo and talk to Steven. One of the options he gives you is Transfer Data, where you can select one of your items (Glalie, balls, etc) and it will be sent to your main copy of the game via Pokemon Link. You can only select one item from the demo to transfer per day. Then start the actual game and select Pokemon Link from the main menu to receive your transferred item (like receiving gifts from Pokemon Bank). Glalie will automatically be deposited into your PC.

All of this found by reading the manual for the demo

Ahh, I was looking for it somewhere within the full game. Whoops.