To make 1 pint:
1 lb of apples
1/4 lb of plums, with the pits removed
Run the apples through a juicer. Skim off the foam.
Put the plums in a blender with a bit of the apple juice, and blend until as liquefied as possible. Stir into the apple juice.
Squeeze the juice through a cloth bag to strain. (Squeeze into a bowl or serving vessel).
Serve chilled.
First I want to address the cloth bag thing. You can use what is called a jelly bag, or cheesecloth. What I find works the best is just to make a large, rectangular bag with muslin or fine linen. It's cheap and reusable, you can make it as big or small as you need, and works much better than cheesecloth, which is too loose of a weave.
Other notes. I tried this with two different methods, using apples and plums that were all from the same batches. (Got at a farmers' market, so they were literally each from the same orchards).
I wanted to see if cooked fruit or raw fruit would yield a better flavor. The raw fruit won (which you could have guessed by the recipe above.) You can read all my notes on the matter below.
Ingredients: 1 lb. apples, cored. 1/4 lb. plums, pitted.
Raw method: Put apple through juicer. Skim foam. Liquefy plum in blender. Stir into apple juice. Strain.
Cooked method: Apple and plum in 1 cup water in pot. When water boils, reduce heat to low, cover, and cook for 15 minutes. Apples will be soft. Liquefy in blender. Strain.
Results for raw method: Fast and easy. Easy to squeeze through the cloth. Only bits of plum skin remain from straining. Yields about 1 pint. Thick, but not as thick as the cooked. Sweeter than the cooked. Remained homogeneous after several hours. 12 hours later, slight separation. Top 3/4 was thick, bottom 1/4 was thin, but when drinking there was no discernible difference in flavor or texture between the two liquids.
Results for cooked method: Takes much longer to make, between cooking and cooling before straining. Difficult to squeeze through the cloth. Basically applesauce remains from straining. Thick, creamy texture--almost too thick, like it feels like it needs to be chewed. Yields just over 1 pint. Remained homogeneous after several hours. Mild applesauce flavor. Not as sweet. Can't taste the plums. 12 hours later, still homogeneous.
Maybe better flavor could be had from cooking after making juice, but there's no reason to bother because the raw version is already very good.