If you don't want to read the documentation and just want to install everything in TeX Live, on a Unix-like system, a minimal recipe follows. Windows installation is described separately. On MacOSX, we recommend installing MacTeX.
To acquire the software in the first place, either get the DVD and/or CD from a user group (ideally by becoming a member), or download the ~930MB zipped ISO image from CTAN, unzip it, and mount it (e.g., mount -t iso9660 -o ro,loop,noauto /your/texlive-live.iso /mnt). Details for all this are in the documentation.
Then, to install (comments are in italics):
cd /the/mounted/texlive/distribution sh ./install-tl.sh d (directory settings) 1 /usr/local/texlive/2007 (your installation directory) 2 /usr/local/texlive/texmf-local (your local hierarchy) r (return to main menu) i (install)
It takes about half an hour to copy all the files.
You don't need to change the installation directories if this is a first-time install, or the defaults shown above (/usr/local/texlive/2007 and /usr/local/texlive/texmf-local) are acceptable to you.
If you need to configure for 8.5x11 letter-size paper, follow up with
something like this:
texconfig paper letter
(Use the syntax for your shell, your own chosen directory, and your own system name instead of i386-linux, naturally.)
If you are installing for a multiple-user site instead of personal use, run texconfig-sys instead of texconfig.
Multiple TeX distributions: only one TeX distribution can be active at a time, because all the TeX distributions use the search path to find their programs. This means that to switch from one TeX to another, e.g., between the native TeX Live and a TeX provided by your operating system, you must (at least) change the search path.
Please email comments or suggestions. And please read the documentation for more details.