The first thing that you need to do is to get yourself a Wii video game console. This is of course an obvious thing to do. Since Nintendo has released a successor of Wii video game console, Wii U, last year, you will be able to get a ready good deal on it as it is considered a bit out-dated. Even though the hardware is a bit old, it still has a great entertainment value, especially with a huge list of fun games available on it. Most of the games are designed to offer a family entertainment experience instead of simply focusing on an individual. Make sure you buy more than one controller to derive the maximum satisfaction off the console and its games.
Once you have bought the console, purchase the Mario Kart Wii game. This too is an obvious thing to do. The game was released in 2008, so there is good chance that you will be able to find someone who would no longer be interested in playing it anymore and therefore willing to sell it at a cheap price. If you find such a deal, go for it, otherwise buy it from any shop where it is available. If you are unable to find a copy in a local video game shop, then order it online.
Now that you have the console and the game, you can get down to unlocking Diddy Kong. In order to get the monkey behind the driving wheel, you will have to compete in and win all retro 50cc Cups. Winning these races will not be very easy, which is why you will need to practice and hone up your skills.
Once you have won all retro 50cc Cups, you will find Diddy Kong available for selection on the character select screen.