Specifically for Mystery Gift..
1. Start up your game.
2. When it says to press start, press it to get to the main menu.
3. From the Main Menu, scroll down to Mystery Gift.
4. Select Mystery Gift, and then select Receive Gift.
5. If it asks if the communication channel should be open, just click Yes.
6a. If it is a Wifi event (meaning you can receive it from home), select Get Via Nintendo WFC.
6b. If it is a Wireless event (meaning if you have to go to Gamestop or something to receive it), then select Get Via Wireless.
6c. If you are doing it with a friend (so you need to be within range of each other), select Get Via Infrared.
7. Wait for the Mystery Gift to be loaded, and then download it.
8. Go to a Pokemart (or Pokecenter for Black and White, I suppose) to receive the gift. If it is a Pokemon, make sure you have room.
I believe that about sums it up. Feel free to correct me if I'm wrong.