Basically to get the Homebrew Channel going you need to run its ELF installer via the Twilight Hack. Here's a pretty good tutorial I followed:
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And to learn how to run ELFs with the Homebrew Channel (not using the Twilight Hack), go here and read my post:
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The HC tutorial is a little technical, but if you're capable of meeting all the requirements then you can run your ELFs from the channel rather than the TH. I'm not sure if all ELFs will work this way, but I got the much-discussed WAD installer to run under it, and most people were saying it wasn't possible to run it under the HC.