Allow me to preface this saying I really haven't used Linux since the first distro of Lindows was released, and haven't used the cli since DOS 6.2 and my Commodore Amiga days. So, long time for both.
I have found that Yumi doesn’t work as expected with TinyCore
However, the Option 2 guide using Rufus portable works great
Here
http://wiki.tinycorelinux.net/wiki:install_usb_stepbystep?&#option_2
Took me a day of searching the site to find this excellent post! I tried Yumi, core2usb, isotousb, and a few others, including rufus. Now that I know what to modify, boots into the gui.
NOW the problem is, when I install it onto the harddrive, it asks which folder to copy extensions from. Huh, that's a GREAT question! Where *are* the extensions located? I download the newest core to install from the web, take the default suggestions for everything else. I leave the extension box empty because I don't know what subdirectory to find them in. I hit my install button, goes to the hd like a champ!
I then shutdown the system, remove the usb drive, power on, and am back at the tc$box.