MacTeX is your friend! This contains the latest TeXLive distribution.
Personally, I edit using Aquamacs with AUCTeX and friends enabled.
As I know, TeXworks, (g)VIM, Emacs, gedit, SciTE, TeXmaker,... , all work fine with CJK.
I usually use TeXworks and gVIM on both Windows and Linux. Just set UTF-8 encoding as default, everything will be fine.
However, I always use Chinese version (locale) of Windows/Linux. You might meet some font problem.
In VIM, you should at least set proper guifontwide in .vimrc. Moreover, you may also need to set encoding, fileencodings, ambiwidth and formatoptions.
In TeXworks, one cannot set different font for wide and non-wide charcters. Be sure that the font you set support CJK symbols. And you'd also set UTF-8 encoding.
Things are similar when using other editors.
For Ubuntu, you'd install poppler-data to display CJK glyphs in some PDF files in Evince.
As Caramdir already pointed out, don't use texlive package through apt-get. You'd better use full TeX Live from TUG. xeCJK with XeLaTeX is recommended.
Best Answer
Eclipse strikes me as an odd choice of an IDE to use for LaTeX, but I guess it should work, since the steps in producing a LaTeX-generated document are quite similar to those involved in producing a computer program.
The first step is obviously to make sure you have Eclipse and LaTeX themselves installed. Then, if you haven't already done so, you should definitely install the TeXlipse plugin or some equivalent, which provides syntax highlighting and autocompletion, among other things. (Without it, Eclipse would be nothing more than a glorified text editor and in that case you'd be better off just using a plain text editor.) The TeXlipse user manual provides a good description, including screenshots, which I would recommend you follow to the letter, as all the enabled features will most likely be useful to you. Once you've got the plugin installed and configured, just open a project and try compiling it to make sure it works and to get a sense of how the process works.
Eclipse is, of course, not the only IDE you can use for LaTeX; there are specialized LaTeX editors available. My favorite happens to be Kile, which also provides syntax highlighting and autocompletion, as well as a LaTeX symbol list and graphical build commands that are designed specifically for the LaTeX toolchain. It is based on KDE, so if you are using the default graphical environment for Ubuntu (Gnome) you may have to install some - okay, a lot of - extra packages to use Kile, and it's your choice whether that's worth it or not.