I will give a bit more detail.
Install mkisofs-tools before beginning.
The first part is mounting the iso so you can access the files.
Create a new directory in /home/tc called dl (using a file manager).
Copy tinycore_3.6.iso to /home/tc/dl
Create a new directory in /home/tc/dl called tmp.
Use these commands in the terminal to mount it.
sudo su
cd /home/tc/dl
/bin/mount tinycore_3.6.iso tmp
You can now access the files on the iso, from the directory /home/tc/dl/tmp
Everything is in the directory boot.
Create new directories, let's use /home/tc/new-iso/tmp
Copy the contents of /home/tc/dl/tmp (the directory boot) to /home/tc/new-iso/tmp
The next step is to add apps.
Copy your entire tce directory (/mnt/sda1/tce may be something other then sda1) to /home/tc/new-iso/tmp.
You should now have 2 directories, boot and tce.
You now have all of the apps from your computer to the directory for the new iso.
The next step is to make a new iso.
Copy and paste this to the terminal.
http://wiki.tinycorelinux.net/wiki:mousesudo su
cd /home/tc/new-iso
mkisofs -l -J -V TC-custom \
-no-emul-boot -boot-load-size 4 -boot-info-table \
-b boot/isolinux/isolinux.bin -c boot/isolinux/boot.cat \
-o TC-remastered.iso tmp
Burn this iso to a cd and see if it works.
After you have done that you can experiment with other options.