You will need at least a pound of elderberries for this recipe, and preferably three pounds, so you have enough to last a while. I use a food mill to extract as much juice as I can from the berries, but if you don't have one you can use a jelly bag.
You will need to remove the berries from the stems; elderberry stems are toxic. (I go through some tricks on destemming elderberries here.) It should take you about 45 minutes to an hour to destem 3 pounds of elderberries, which equates to about a half a normal paper grocery bag.
At this point you can empty your berries into a large bowl of ice water. Weird debris will float, like dead flower husks, bugs, etc. Pour this off.
Pour the elderberries into a large pot and either mash them thoroughly with a potato masher, or, better yet, with an immersion blender. Only break up the berries for a few seconds using the immersion blender, and use it on low setting. You don't want to grind up the seeds, which are bitter.
Bring the elderberries to a boil, stirring often. Now, if you are using a food mill, set it up with its finest plate and pour the elderberries into it. Run the food mill until the mash is pretty dry, then squeeze out any remaining elderberry juice. You should have a little more than 1 quart. Pour the juice through your finest mesh sieve to catch any stray seeds or pulp.
If you are using the jelly bag method, mash the berries again after they've boiled, then pour them into a jelly bag suspended over a large bowl. Let this drain up to overnight. You should have a little less than 1 quart. You don't need to strain the juice the way you do with the food mill method.
Return the juice to the (cleaned) pot and add an equal volume of sugar, normally about 4 cups. Bring to a boil until it froths, skim the froth, then turn off the heat and pour into clean jars. Always use a new canning lid when you are making this syrup, unless you plan on eating it in the next few weeks. Seal the jars and let stand until the lids pop. They will keep for a year on the shelf or in the fridge.