You need to install Xvesa plus a window manager. It's been a while since i set up a new Xvesa system. If you had downloaded and installed the 15mb Tiny Core from
http://tinycorelinux.net/downloads.html it would essentially give you a basic Xvesa graphic system with flwm_topside window manager, one of the leanest available.
So if you're new to Tiny Core, it may be easier to start fresh and install the 15mb Tiny Core variant outlined. Otherwise use tce-load -wi (wget install) to download additional software for graphics, provided you have a working wired connection. This *should* work but it's been a while:
tce-load -wi Xvesa Xprogs Xlibs flwm_topside wbar aterm
Here's the entire default Tiny Core onboot.lst if above don't work and you need to install more. Not sure why it's so complicated now. Before i just had about half a dozen extensions loaded to get into barebones Xvesa. Many of these may already be dependencies of Xvesa, Xprogs and flwm_topside.
aterm.tcz
fltk-1.3.tcz
flwm_topside.tcz
freetype.tcz
imlib2-bin.tcz
imlib2.tcz
libfontenc.tcz
libICE.tcz
libjpeg-turbo.tcz
libpng.tcz
libSM.tcz
libX11.tcz
libXau.tcz
libxcb.tcz
libXdmcp.tcz
libXext.tcz
libXfont.tcz
libXi.tcz
libXmu.tcz
libXpm.tcz
libXrandr.tcz
libXrender.tcz
libXt.tcz
wbar.tcz
Xlibs.tcz
Xprogs.tcz
Xvesa.tcz
Then reboot, should get graphics. If not then at terminal:
desktop=flwm_topside
startx
...and i think running setup.sh will allow you to choose resolution:
setup.sh
If Xvesa doesn't give desired graphic resolution then upgrade to Xorg. There's also framebuffer, also lightweight, but i don't have experience with it and always found Xvesa easiest.
Tiny Core can be complicated to set up initially. For example, if you don't have a persistent system then everything downloaded and modified will be lost on reboot. If you're serious about getting a TC system running review the Core book linked on the homepage.