What package format does tiny core use
TinyCore uses two different package types: .tce (gzipped tar files) and .tcz (cramfs or ziofs compressed mountable images). See
http://tinycorelinux.com/concepts.html for a description of these types and the wiki for an instruction how to create new ones and submit them to the official repository:
http://wiki.tinycorelinux.com/tiki-index.php?page=Creating+Extensionsand how do i install packages that i have downloaded on another computer and put on a usb?
To install .tce packages from outside the official repository, start the appbrowser then click on "File->Install Local". For local .tcz files: these are not really "installed" at all, you just have to copy them into your "Persistent Personal Repository" (PPR).
This mixed up extension concept is quite flexible but a little bit confusing for beginners. I have to admit that I do not have a good understanding of this PPR either, so I really do hope that some day someone will draw some nice pictures and add them to the "Tiny Core Concepts" page so that those who learn with their eyes have a better chance to understand the difference between these "modes of operation".