To handle and apply patches, BRL-CAD uses Subversion.
You will need to install Subversion (Often abbreviated as svn).
If you're on a Debian/Ubuntu system you can get it by running:
sudo apt-get install subversion
You can obtain the latest version of BRL-CAD by running:
svn checkout https://svn.code.sf.net/p/brlcad/code/brlcad/trunk brlcad
If you are in the folder where the "brlcad" folder is and you run that command, svn will only download updated/modified files.
In order to submit a patch it is important to have the latest version of BRL-CAD. After you have done that, you get into the brlcad directory and run
svn diff > ~/first.patch
This will create the patch file in your user's home. The patch is in text format and you can read it to make sure it contains what was intended.
If you added a new file and want to include it in the patch, run
svn add myfile.txt
However, if you removed a file and want that to be included in the patch, run
svn remove myfile.txt
To submit a patch to the BRL-CAD tracker you must first create a sourceforge account. Of course, if you have one already, you don't need to create another.
Now, you can submit your patch on the BRL-CAD tracker by clicking "Create Ticket".
You should use the description field to explain what you did there and, if necessary, what isn't working.