That depends on the situation:
1. Missing kernel module that's available in the linux kernel but it's just not compiled for tinycore (take a look at all *-2.6.33.3-tinycore.tcz extensions before assuming that!)
1.1. Download kernel sources from
http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/3.x/release/src/kernel/ and install compiletc.tcz extension
1.2. Edit the kernel .config e.g. CONFIG_MY_MODULE=m
1.3. Run "make modules"
1.4. Find your module, gzip it: mymodule.ko => mymodule.ko.gz
1.5. Put it in the right place of the filesystem, e.g. /usr/local/lib/modules/2.6.33.3-tinycore/...
1.6. In case you want to have it always available then back it up or create a module extension or recreate initrd tinycore.gz to include it
2. Modules from other sources
2.1. Install compiletc.tcz and linux-headers-2.6.33.3-tinycore.tcz
2.2. configure and make (like every other source code)
2.3. issue make install to see where it belongs or just put it there yourself
3. Drivers
3.1. Compile them like every other source code and put them into an extension (how you can do that is written all over the forum and in the wiki