Online games come in a variety of different forms. Almost all are downloaded right from the Web as either freeware, shareware, or demos. Other game programs can be purchased on CD-ROMS in a retail store. You can download and play freeware games without any payment or fees due to the author. Sometimes the author asks that you register the program by sending a post card or email message letting him know you are using his program.
Freeware games are full versions with no crippling limitations.
Shareware versions also can be downloaded right from the Internet. These usually require a registration fee that is paid directly to the author. Other shareware programs will only allow you to play to a set level. To go further, you must pay the registration fee. The author then sends you a copy of the program that has no limitations.