Eco-friendly birthday parties require no more planning than any other birthday bash -- it's just a different flavor. Rethink the party from the invitations and the decorations to the foods you serve.
The easiest way to turn a birthday party "green" is to replace the paper items with those that are sustainable (think reusable or recyclable) instead of disposable. For example, think about your tablecloth. Sure, the $5 tablecloth from the party store is easy to dispose of, but instead, consider using a reusable, washable sheet or other fun fabric.
Also, skip all the crepe paper and balloons. Hang up Japanese paper lanterns instead (they're reusable!) or assemble homemade decorations made from recycled paper.