composting advice, please!

Hi there, can anyone give me advice on how to start composting? I hate throwing away food scraps that could otherwise be used. The problem is, I live in an apartment building, no garden, and very little yard. I looked up composting on the Seattle Public Utilities site, and I see I can buy a compost barrel, but what would I do with the compost when it was ready? Could I take it to my neighborhood P-Patch (I’m on the waiting list), or somehow find someone who could use it for their garden? I would love to get the other folks in my apartment building involved, if I could figure out what to do with the compost. Thanks for any tips you can provide!