Demos of games allow you to play a small section of the game in order to see if it works on your computer and if you like it. After you complete the demo or run out of time in the case of "time limited' demos, you have the option to get the full version of the game. On some digital distributor websites, such as Steam, the full game downloads automatically with the demo and you simply need to purchase it to unlock and turn the demo into a full-version game.
Play through the demo game and see if you like the game and that it runs well on your computer.
Click on the "buy now" or "purchase" link that the demo shows after you finish or exit it. The demo will likely display a list of features and extras that the full game has and provide you with a link to the website where the full game can be purchased.
Log into the website or create an account with the game's creators' website. Enter your personal information into the registration fields if you are a new user. Add a valid e-mail address that you check regularly as it's likely that the activation code to turn the demo into a full version will be sent to this address.
Make the payment using one of the supported payment options. Check your e-mail for a confirmation that the money has been received and your order is being processed.
Enter the registration number you will receive via e-mail into the space provided for it in the game. You will receive detailed instructions with the key on how and where to enter it to turn your demo game into the full version.
To make the demo game into the full version using Steam, simply right click on the game icon in your library and select "purchase full game." Make the payment and you can start playing the full game immediately.