Download, Drag, and Drop
Download the current release from the download page. Note that GnuCash 3 and later are supported only on OS X 10.9 (Mavericks) and later; users of Mac OS X 10.5 (Leopard) - 10.8 (Mountain Lion), including those with PowerPC Macs, should be sure to download GnuCash 2.6.21, paying attention to the supported architecture.
Open the disk image and drag GnuCash from there to your applications folder. If you want to retrieve stock prices from the web, double-click on Finance Quote Update. This will run a terminal application, even opening Terminal for you. It's a bit of a pain and requires that you have Xcode installed. We're sorry about that, but we haven't been able to figure out a better way.
Upgrades: Same procedure: Download, drag, and drop. If, and only if you're upgrading from a version before 2.4.0, double click on Upgrade Dirs in the disk-image.
Instructions for building a complete Gnucash application, including bundling it for distribution, are at MacOS/Quartz.
MacPorts is a parallel package manager to make macOS work like Linux. See MacOS/MacPortsDetail for more information.
If you encounter problems, please check the mailing list archives first and then, if your problem cannot be resolved based on the information found there, report it to the mailing list. Please do remember that GnuCash developers are volunteers and are not responsible for your computer; as such, your help (in the form of exhausting readily available resources before asking for help and in asking for help in a clear manner) is appreciated.