Oleo saccharum (say "OH-lee-oh SAK-ah-rum", Latin for "oil sugar") is the oldest trick for getting the smell of citrus into a drink. You peel the fruit, bury the peels in sugar and wait. The sugar pulls the aromatic oil out of the skin and slowly dissolves into a thick, fragrant syrup. There's no heat and no alcohol, which makes it as useful in a mocktail or a pitcher of lemonade as in a punch.
The yellow or orange part of a citrus peel is full of tiny oil sacs. Sugar draws water out of the peel by osmosis, and the oil comes with it. Fresh juice gives a drink sourness. The peel gives it the bright, perfumed top note you smell when you squeeze a twist. Oleo saccharum is how you bottle that note.
The old punch writers used it because it let them use the whole fruit: the juice for the sour part and the peel-sugar for the sweet, aromatic part. It came back into home bars after David Wondrich's book Punch brought it to a new audience.
Recipes differ, so here is the common middle. Weigh the peels, then use about the same weight of white sugar, a little less or more to taste. Rest the mix covered for at least an hour or two, longer if you can: 4 to 6 hours is a common minimum for a proper pool of syrup, and overnight is a classic. Stir or press it now and then. When most of the sugar has dissolved and there is a puddle of liquid in the bowl, remove the peels. The puddle is your oleo saccharum.
It is strong and very sweet, so many people stretch it with a little water. One common suggestion is about half as much water as sugar for a thick syrup; go to equal parts for something closer to a 1:1 simple syrup. The builder below does the sums.
Then juice the peeled fruit. Don't throw it away: the juice is the sour half of your drink.
Treat it as a stronger, more fragrant stand-in for simple syrup. A teaspoon or two in a glass of sparkling water with a squeeze of the juice already tastes like a proper lemonade. In a sour or a daiquiri, swap it for the syrup and start with a bit less, since it is sweet and strongly flavoured. In a punch, it is the base the rest is built on. For an alcohol-free version, use lemon, orange or grapefruit oleo with tonic or soda, a little bitter, and plenty of ice.
Mix citrus: lemon and orange together make a rounder syrup, and lime is thinner-skinned so it needs less sugar per fruit. Small variations are worth a notebook entry.
If you're short on time, there is a quick version: pour a little hot water over the peels and sugar to speed up the dissolving. You trade some of the fresh oil for speed, but it works for a party. If a batch comes out bitter, you probably had too much pith or left the peels in the syrup for days. Next time remove them once the sugar has dissolved.
Drinks made with it are for adults only when alcohol is in them. Without alcohol, it is simply a flavoured syrup, but it is still sugar, so measure it like any sweetener.