With all due respect, if you're just getting into assembly language programming, I really wouldn't recommend attempting to develop an operating system.
However, as per your question; nasm is installed simply by unzipping the archive, and posssibly compiling (did you get the source archive? If so... uhm... Read The DOCS! "make").
I haven't used TASM in quite a while, although I still have a _registered_ version of 4.0, which came with its own installation program. I'm assuming all other versions would as well (ie, just type "install" would probably suffice).
Assembling is a simple matter of:
tasm file.asm -o file.obj
or
nasm file.asm -o file.[ext]
where .ext can be any supported output format (binary, elf, coff, etc). Make sure you set that format with... uhm... -f, I believe. Again, read the docs dude. All this information is available in the zip's... how do you think the rest of us did it?
Which assembler do you have, or do you have both? Nasm is a considerable better assembly then the free version of tasm floating around, in my opinion. However, I mean no disrespect to TASM... I love that assembler, and if you can get a new version (ie, pay for it), it's worth the money. Borland doesn't make bad products!
Jeff