Download the Mac GNU Privacy Guard, or in short: MacGPG. You can retrieve it from here.
You need the 'GNU Privacy Guard' as well as the 'GPG Keychain Access'-tool.
Download the GPGMail plugin
Download the GPGMail plugin for AppleMail. You can retrieve it from here.
Step 2: installing
Doubleclick on the 'GnuPG1.2.3.dmg'-file. The filename is different for newer versions (the '1.2.3'-part). This clicking will 'mount' the '.dmg'-file onto your system, you don't need to understand this. A white floppydrive-like icon will appear on which you need to doubleclick.
After that a window will appear with a lock and a couple of icons. Doubleclick on the 'GnuPG for Mac OS X 1.2.3.mpkg'-icon.
A screen will appear that asks you to enter your password. Here, enter the password you would normally enter when installing software (as you're doing right now).
Then press 'Continue' twice. You'll be asked then to agree with the license of the software. Press 'Agree' to continue.
A screen will appear where you have to select on what disk to install the GnuPG software. If there are multiple harddisk-icons you'll probably know yourself what disk to install to, otherwise just click on the harddisk icon, a green arrow will appear on the disk. The last step is pressing the 'Install' button, the system will now install the GnuPG software. Press 'Close' to finish the installation.
Now 'unmount' the GnuPG1.2.3.dmg'-file by dragging the icon to the thrash-can.
Install the GPG Keychain Access tool
Doubleclick the 'GPG_Keychain_Acess.0.7.0.1.zip'-file. The 'Stuffit Expander' appears and unpacks the zip-file into a 'GPG_Keychain_Access.0.7.Folder'. Open that folder and in that window open the 'GPG Keychain Access'-window. Then drag the 'GPG Keychain Access'-file (the keyring) to the desktop. Now you can drag that 'GPG_Keychain_Access.0.7.Folder' to the trashcan.
Install the GPGMail plugin
And finally: install the GPGMail plugin for AppleMail!
Doubleclick on the 'GPGMail-1.0.2>-10.2.dmg'-file. The filename is different for newer versions (the '1.0.2'-part) and also different if you downloaded the file for a more recent MacOS X version (the '10.2'-part). This clicking will 'mount' the '.dmg'-file onto your system, you don't need to understand this. A white floppydrive-like icon will appear on which you need to doubleclick.
After that a window will appear. Look for the 'Install GPGMail'-icon and double click on it. A window will appear which welcomes you to do the GPGMail Installer. Click on 'Run'.
A window will appear where you need to find the 'Mail'-application. Click on it and clik the 'Choose'-button. Your system will start to rattle.
When it is done, a window will appear that tells you everything was installed fine. Click the 'Launch Mail' button.