Download, Drag, and Drop
Download the current release (either Intel or PowerPC, depending on your architecture) from the download page.
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.
Readme: Be sure to read the Readme in the disk image. It has extra information about that particular release of Gnucash.
SQL Backends: The only SQL driver included with the downloadable version is for SQLite3, which creates a local file. If you really need to use a MySQL or Postgresql server you'll have to build the drivers yourself. Instructions may be found in Quartz Build page. (Remember that Gnucash is single-user even when connected to a database server. That means only one user can be connected to a database at a time.)
Instructions for building a complete Gnucash application, including bundling it for distribution, are at MacOS/Quartz.
There are other ways to get Gnucash on your Mac. These instructions may be old, but the procedures haven't changed much.
Fink is a package-management tool making it easier to install all your favorite *nix tools and libraries under MacOS. It's also the quickest and easiest way to get at least some version of GnuCash running on a PowerPC Mac (Intel Mac users see below.)
Follow instructions to install fink from source. You will need to install Apple's Xcode Tools before you can install anything from source (aka: compiling). Be sure you have already installed Apple's Xcode Tools (it is on your Leopard DVD) before trying to install fink from source.
Other Fink options
Further discussion of semi-manual ways to compile GnuCash using Fink tools can be found here. Most of that information is generally outdated since the availability of the gnucash2 package. However, it may still be useful in some cases, for example if you would like to use Fink in conjunction with compiling a version of GnuCash newer than any available in a Fink package.
MacPorts (formerly known as DarwinPorts) is another, parallel package manager for Mac OS. 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.