So I jumped right into discussing infusion flavors and the dynamics they add to a liqueur without talking about the almost forgettable ingredient of simple syrup. There are many flavored liquors in the world, but a liqueur or cordial is partially sugar. In most cases that means simple syrup. The ratio in most liqueurs between alcohol infusion and simple syrup is 50/50. A skilled home liqueur maker might tweak those ratios to get a more specific effect, but it's a good starting point.
There are two types of simple syrup that I tend to use in my house. The first and easiest to make is plain simple syrup made with white sugar. The recipe for said syrup is:
1 part white sugar
1 part water
boil until completely dissolved
There really isn't much to say about plain simple syrup other than I primarily use it to pair with light fruity liqueurs. Strawberry, lemon, peach and similarly delicate flavors.
The second type of syrup I make is Turbinado syrup. The recipe for that is follows:
1 part organic evaporated cane juice
1 part water
Bring ingredients to a boil, then reduce to a steady simmer. A film will develop on the top of the syrup that is very similar to the scum that develops on the top of chicken stock. Skim the froth off with a spoon or similar implement and discard. Continue to simmer until the syrup is completely clear and froth is no longer developing. Depending on how much syrup you are making, and how long this process takes (different turbinado sugars have different concentrations of impurities) you might need to add some extra water to compensate for the moisture that boils off.
This syrup is nice because it is easy to find organic turbinado sugar. Turbinado also brings a nice earthy roundness to the flavor party. This syrup pairs well with cacao, coffee, vanilla, nut infusions other earthy flavors.
The other thing you can do with these syrups is do a heat steeped flavor infusion instead of infusing your flavor in the alcohol. Ginger works very well for this, as does lemon zest. I try to keep ginger turbinado syrup around whenever I can. The water and sugar infusion draws very different flavors out of your ingredients because of different solubility profiles in the flavor molecules. A ginger syrup can add a very different flavor profile to a liqueur than a ginger alcohol infusion. So it's something to consider experimenting with. I recommend infusions that do not involve fruit as they will add pulp to the syrup and that will effect the liqueur texture.