Check a few FAQs from the main CycloDS website, but it's usually as simple as downloading the homebrew application, and extracting all the files to the root of your SD card. If you prefer, you can put the .nds files that come along with the homebrew downloads into a seperate folder named "homebrew" for example.
That way, when you boot up your Cyclo, and go into the rom list, you will have a folder called homebrew, and you will be able to launch your homebrew games from it.
As far as what games/applications too download, I would check this thread:
http://gbatemp.net/index.php?showtopic=70463
and this thread:
http://gbatemp.net/index.php?showtopic=82722
But, my personal favorites include StillAlive, Videogame Hero, Moonshel, DSOraganize (if you have wifi), WC3: TD, and Whee!.
I hope this helps.