How do you buy compound coins?

Could you elaborate on the process of purchasing compound coins in the cryptocurrency market? I'm particularly interested in the steps one needs to take to acquire these tokens, starting from the initial research to the final exchange or wallet transfer. What are the key factors one should consider while choosing a platform or exchange to facilitate this transaction? Additionally, are there any specific risks or challenges associated with buying compound coins that investors should be aware of? Your insights would be greatly appreciated.