To open the download options panel, please log onto your account and click your game in your Library section:
From there, you've got these options:
1a) We recommend using GOG Galaxy - our optional client which makes downloading and installing games as convenient as possible. Just go to https://www.gog.com/galaxy then download and install it on your system. Afterwards, just launch it, log in, and you can install games directly from your 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:
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, with your browser only. Just open your account:
click the game and the installer you want.
If a game contains multiple "part" files, you need to download all parts before you can start installation.