Cygwin
Here are some steps to use Cygwin for patching in Windows. There is a videocast on Installing Cygwin on Windows XP that covers installing Cygwin but not actually using it.
1. In your c: drive, create two folders; one named C:\cygwinstuff and another named C:\patchfiles
2. Go to www.cygwin.com and download the setup file.
2. Click on the file downloaded in step 2 to start the install
The next few steps will walk you through the install process for Cygwin.
4. Choose Install from Internet
5. For Root Install Directory: Choose C:\cygwin
6. For Local package directory, choose c:\cygwinstuff -- the folder you created in step 1.
7. Choose the appropriate internet connection -- for most of us, that's the Direct Connection
8. Choose a download site -- I generally pick one at random, but for those of you who are more precise, you can use the domain names to try and choose a site on the same continent.
9. Select packages: This is where things can get tricky. Just make sure to select the patchutils under the Devel section.
Note that, when installing packages for the first time, setup.exe does not install every package. Only the minimal base packages from the cygwin distribution are installed by default. Clicking on categories and packages in the setup.exe package installation screen will provide you with the ability to control what is installed or updated. Clicking on the "Default" field next to the "All" category will provide you with the opportunity to install every Cygwin package. Be advised that this will download and install hundreds of megabytes to your computer. The best plan is probably to click on individual categories and install either entire categories or packages from the categories themselves.
Once you've installed your desired subset of the Cygwin distribution, setup.exe will remember what you selected so rerunning the program will update your system with any new package releases.
10. Begin the install.
11. Once Cygwin has installed, move the file(s) you want to patch, and the patch file, into the C:\patchfiles folder you created in step one.
12. Open Cygwin. Cygwin gives you what you have been looking for: the command line. You will need the following commands:
ls -al-- lists the contents of your current directorycd ..-- moves you up to the parent directory (note the space between cd and .. if you come from a DOS background!)cd foldername-- moves you to a specific folder visible from your current directory
13. When you open Cygwin and type ls -al, you will see the contents of your current directory. Different versions of Cygwin start you in different directories. Regardless of where you start, you can use cd c: to navigate to your C: drive (under Cygwin, this will be called /cygwin/c).
14. When you are at C:, you will be able to see the patchfiles folder you created in step one. Use cd patchfiles to navigate into this folder.
15. Type ls -al. You should see the files you moved into this folder in step 11.
16. Type patch filetobepatched < patchfile or patch -p0 < patchfile if there are many files to be patched.
17. Before you copy the patched file(s) to your production (live) site, make a backup copy of the original, unpatched file(s). Better safe than sorry, and you never know if/when you might need them.
These instructions ought to get you started.
For a more comprehensive overview of the options available while patching, see the patch manual (man) page.

Two things to mention for the non-Cygwin user (like me):
1) < is the "less than" sign (<).
2) Make sure you have extracted your ProjectPier installation files with the folder structure intact.
Thanks for this great guide!