While most seasoned veterans probably prefer a good old makefile, if you're new to ARM you'll appreciate the hand-holding an IDE can provide. We'll be using NXP's free LPCXpresso IDE in this tutorial, which is based on Eclipse and GCC, and works with all of their recent chips.
In order to download NXP's free LPCXpresso IDE, you do need to create an account on Code Red's website (who are now owned by NXP), at https://www.lpcware.com/lpcxpresso/download
While registering sucks, LPCXpresso is still the easiest free tool using an open source toolchain, and you can easily break out of it once you're a bit more comfortable with ARM and GCC, creating your own makefile and linker script, and LPCXpresso is just a bit of icing on top of the Eclipse + GCC cake.
An advantage of LPCXpresso is that it includes a relatively easy to use installer for Linux, Windows and Mac OS X, so you're free to use the toolchain and IDE on any major platform.
After registering, you should see a download list similar to the following: