Sorry if it wasn't clear. For HG/SS all you need to do is select 'Mystery Gift' from the game's start-up menu (the bit with the blue background), then choose 'Receive via Nintendo WFC'. You will then receive Jirachi and can pick it up from the pokemart.
For Diamond/Pearl/Platinum, it's a little different. Read the bit on our walkthrough page under "Obtaining Mystery Gifts". You need to go to that guy and give him the phrases in order to get Mystery Gifts. Then save your game, restart and do the same as above - select 'Mystery Gift' from the game's start-up menu.