From Eggdrop Wiki

Step 1: Obtain the patch

1:30pm simple@server [~]$ cd eggdrop1.6.19
1:30pm simple@server [~/eggdrop1.6.19]$ wget http://www.techmonkeys.org/~tothwolf/eggdrop/eggdrop1.6.19+runtime-threads.patch.gz
--13:30:10--  http://www.techmonkeys.org/~tothwolf/eggdrop/eggdrop1.6.19+runtime-threads.patch.gz
           => `eggdrop1.6.19+runtime-threads.patch.gz'
Resolving www.techmonkeys.org... 24.72.125.129
Connecting to www.techmonkeys.org|24.72.125.129|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 81407 (79K) [application/x-gzip]

100%[====================================================================================>] 81,407         --.--K/s             

13:30:11 (91.12 KB/s) - `eggdrop1.6.19+runtime-threads.patch.gz' saved [81407/81407]

1:30pm simple@server [~/eggdrop1.6.19]$ gunzip eggdrop1.6.19+runtime-threads.patch.gz
1:30pm simple@server [~/eggdrop1.6.19]$ patch -p0 < eggdrop1.6.19+runtime-threads.patch
patching file ./aclocal.m4
patching file ./config.h.in
patching file ./configure
patching file ./configure.ac
patching file ./doc/COMPILE-GUIDE
patching file ./doc/html/compiling.html
patching file ./src/bg.c
patching file ./src/chanprog.c
patching file ./src/main.c
patching file ./src/patch.h
patching file ./src/tcl.c
patching file ./src/tclegg.h
1:31pm simple@server [~/eggdrop1.6.19]$

Congratulations, your source is patched. Configure and compile your eggdrop as you would normally.