To open the download options panel, please log in to your account and select your game in your Library section: https://www.gog.com/account. From there, you have the following options:
1a) We recommend using GOG Galaxy - our optional client which makes downloading and installing games as convenient as possible. To install the game using Galaxy, click on "DOWNLOAD AND INSTALL NOW".
You can also download Galaxy separately, after going to https://www.gog.com/galaxy. Install the client on your system, then simply launch it, log in, and install your games directly from the Library section.
1b) You can also download standalone installer files and bonus goodies via GOG Galaxy, by clicking the game in your Library, going to MORE > Backups & goodies and clicking the files you want.
2) The GOG Downloader, our legacy application which is an alternative to Galaxy. It's lighter, but also provides download resuming, as well as error protection. You can find the Downloader's installer here: http://www.gog.com/downloader. Once it is installed, please open your account: https://www.gog.com/account, click the game in your Library and select More > GOG Downloader Links. You will be able to start your download there.
3) You can also download the files manually, using your browser. Just open your account:
https://www.gog.com/account, click on "Download offline backup game installers", and then click on the files on the list to download them.
If a game contains multiple "part" files, you need to download all parts before you can start the installation.