Once you have finished placing and paying for your order, the game you bought will be added to your GOG account and can then be downloaded - you can either use the Galaxy client, your browser, or the legacy GOG Downloader to do so. If you want to learn more about how to download your purchased game, you can find more information in this support article.
If you can't see the game in your account's library, your order might still be processing; unfortunately, this can sometimes take up to two hours. Should the game still be unavailable after two hours, please try to refresh your account manually by clicking here. If this also doesn't help, please contact our support team directly so we can investigate the issue.