Star Airline offers flight to Juliaca. Peruvian not.There is bus from Juliaca to Puno
It is very difficult to book through star airline's web although the price is very good.
Finally, i found Star airline's US rep. in Miami. But the price is much higher.
Two flights Lima- Cuzco round trip and Lima-Iquitos round trip cost $180 on websie but $330 with the representative in Miami. But still less expensive than LAN and Peruvian web
You may book the flights with travel agency at Lima airport, as advised by many people. Now i understand why many tourists book fights and trains after they arrive Peru although the deals online are good.