In order to apply patch files on your eggdrop (or any other source) you must have a utility called patch. Type:
patch -v
on the machine where you have your eggdrop. If the response is something like "Patch version 2.1" or a later version, then you already have the right thing! If you get some other kind of noise output, you probably will have to find a newer version. Check out the patch binaries page, maybe you find one for your system.
After you have the correct patch binary, get the ".patch" file you want. If it is .gzipped, then unzip it:
gzip -d eggdrop1.3.12+all.patch.gz
Uncompress the eggdrop1.3.1.tar.gz file, and untar it:
gzip -dc eggdrop1.3.12.tar.gz | tar -xvf -
Go to the root directory of the just extracted eggdrop distribution:
cd eggdrop1.3.12
Apply the patch:
patch -p1 < ../eggdrop1.3.12+all.patch
If you have downloaded the "patch" binary, you must enter the full pathname of where you have uncompressed it.
Once you have applied the patch, type:
find . -name "*.rej" -print
If it returns a list with filenames that end in the rej extension then the patch didn't apply properly, ensure that the patch is for the version intended, ensure that you have the original source, and ensure that the patch is not corrupted.
If it turns out that the patch was successful then be sure to recompile by running make again. Remember to properly install the new binary/modules.