Take a taxi to the bus terminal in Cusco (Terminal Terrestre). There are several bus companies that go to Cusco. We took an overnight bus with Civa. There is also Oltursa, Cruz del Sur... It is 10-11 hours. The price depends on what kind of bus you choose, how far the seats recline... (anything from $11 to $35 and although you don't have to take the most expensive option the cheapest option might not be a good idea either). Just check the bus company websites.
I did not go from Arequipa to Cusco but again, you would take a taxi to the bus terminal. I believe it takes 6.5 hours.
If you are going to the Colca Canyon you can consider taking a tourist bus from Chivay to Puno: 4M Express or Rutas del Sur. Just check their website to read about stops (they are tourist buses so they make a few stops) and prices.