Ideas for composting in an apartment

Recently Gwen moved to Portland from an 80-acre farm outside of Charlottesville, VA where she did lots of  "green" things, including a chemical free garden, composting, and just being outside a lot since the farm was their backyard. Now she is wanting to compost on a small scale:

"I have a quick question for you, I live in an apartment community and don't have an option for composting large scraps like corn and watermelon.  I would love to compost, but don't know what to do with my goodies.  I feel so horrible everytime I have to throw veggie and fruit parts away.  Do you know of any good options for me?"

Does anyone have a similar challenge or any ideas for Gwen? Gwen is also interested in being a part of a GreenGroup in the NW-Portland area. Anyone else?