I've been meaning to document this for my own purposes and I might as well share, so here's a step-by-step, even though this thread seems to have covered all the nuts and bolts.
When I install microcore for use with a gui, I use the steps listed below and it just works. The following steps assume:
a) that you will use grub as your boot loader
If you use a different boot loader, I can't help you.
b) you will use Xvesa
If you use Xorg, you can skip downloadeing Xvesa.gz in step #5 but add Xorg-7.5.tcz in step #6 and list it before wbar in onboot.lst in step #7 BUT NOTE that it has dependencies and you will have to download them (and their dependencies, if any) in step #6 and list them before Xorg-7.5.tcz in onboot.lst in Step #7. You may also have to set up a config file for Xorg. Note that I have never done (used Xorg), so this whole paragraph may be a bit iffy.
c) you will use jwm as your window manager
If you use a different window manager, make sure you satisfy any dependencies it might have. jwm doesn't have any deps.
d) you will use wbar.
If you use something other than wbar, make sure you satisfy any dependencies it might have. wbar doesn't have any deps.
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The steps below work for USB flash drives, virtual disk files (like for qemu) and real honest-to-goodness disk drives (IDE and SATA). Probably other bootable devices as well, but probably not optical disks - I don't think grub works on CDs,
Installation steps:
1) install grub on the boot device if it is not already installed. I'm assuming you've installed it in /boot/grub on the device.
2) create /boot/mc3.0 It doesn't matte what you name it, or even of you put it under /boot but I like to give some clue as to what vesion of tc/mc I've installed - for future reference.
3) create /tce and /tce/optional I always used to use something like /mce3.0 and use a boot parameter to point to it, but its just easier to use /tce and let the system find it.
4) download
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/distribution_files/microcore.gz http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/distribution_files/bzImageinto /boot/mce3.0
5) download
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/microcore/Xlibs.gz http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/microcore/Xprogs.gz http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/microcore/Xvesa.gzinto /tce
6) download
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/tcz/jwm.tcz http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/tcz/wbar.tczinto /tce/optional
7) create text file /tce/onboot.lst containing the following two lines:
wbar.tcz
jwm.tcz
8 ) create/edit text file /boot/grub/menu.lst, adding an entry for your new micrcore installation. Mine looks something like this:
timeout 10
# for booting Micro Core Linux 3.0_32 lem 20100721
title mc3.0_32
root (hd0,0)
kernel /boot/mc3.0/bzImage quiet noutc tz=GMT+5 ssh waitusb=9 tce=LABEL=GREENFOB3
initrd /boot/mc3.0/microcore.gz
9) reboot. If it works, great. If grub never starts, you probably skipped an important step in installing grub - this is a common problem mentioned elsewhere in the TC forums. If it can't find your kernel, then the "root ..." line in your menu.lst file is wrong. If it doesn't load any of your extensions and your are booting from a USB device, you probably need to increase the value of the waitusb boot code in menu.lst.
Its late and I'm tired. I apologize in advance for any typos or omitted steps.