How to cure depression without medicine?

2 ways. 1) psychotherapy - many different varieties. Cognitive, cognitive behavioral, transactional, psychodynamic - you name it, it's out there. Many are very effective. 2) transcranial magnetic stimulation - no drugs are involved. I'm specifically not listing "ect" - or electroconvulsive therapy - because even though its effects are not due to drugs, you have to have them administered for the tx.
Many ways. Exercise, rest, good nutrition (omega 3 fatty acids), social interaction, and pleasurable activities all can help mild depression. The herb st. John's wort and self-help books may help too. More severe depression calls for professional psychotherapy, either individual (1-on-1) or group. A new treatment called transcranial magnetic stimulation (tms) seems to work too.