0. Put your heater control valve to full hot.
1. Remove the expansion tank cap.
2. Drain the system from the engine block drain petcock to the point where the expansion tank has drained as much as it will drain (if you have a stainless steel tank, there will always be about 1-1/2" of coolant in the bottom because of how the bottom nipple is connected to the tank) and some from the block. The goal is to lower the coolant level in the engine coolant passages to below the heater output nipple on the right rear corner of the head. If you get about 5-6 quarts out of the block drain, you got what you need.
3. No need to drain the rad or anywhere else at this step (even though you already did so).
4. Now go up to where the heater feed elbow comes out of the cyl head right rear corner and joins to the feed hose. Put some rags under there, loosen and disconnect the hose from the elbow, and immediately position the hose end as high as it will go, and do whatever you need to to keep it there. Keeping it up high will keep it from dripping and will aid a step below. You should not have much drippage from the elbow, but stuff a rag in there just the same.
5. Place a drain pan at the location under the car where the small heater return hard line is connected to the return hose (as shown in JimD's picture above).
6. Loosen the hose clamp and carefully, ALMOST remove the hose from the hard line, BUT!!! put as little pressure and force as possible on the hard line. Since you are at a significant low point in the heater circuit, you will get some flow from the return hose and a lot of flow from the hard line, so be ready for it. Having the heater control valve open and the heater feed hose disconnected and raised at the head, will allow suction and gravity to pull almost all of the coolant out of the heater feed hose and the heater core, which is exactly what you want if you are taking it out of the car and do not want to make any more of a mess than you have to.
7. Now fully disconnect the return hose from the hard line and your heater circuit will empty out 99%.
8. After it drains, if you wanted to "blow-dry" the heater circuit including the core, rig up a shop vac to blow instead of suck and stick the end of the heater feed hose into the shop vac hose and seal the gap with a rag or whatever for a few seconds. Of course this will blow out liquid/spray from the small hard line under the car so be ready to catch that. If you have a length of heater hose handy you could temporarily fit that to the hard line to help in directing the final flow/spray. You could also use compressed air but a shop vac operates at a lower pressure (less likely to overstress any old delicate joints) and much higher volume which I think is preferable for this task.