I have made a simple syrup and want to make it into a buttercream. I have found recipes that use different things to make flavored buttercream but I just want to make the buttercream with only the simple syrup. Can anyone tell me how to incorporate it the right way?

If you are just talking about using the SS as the liquid, I'd think you could just not use your water (or milk, cream, whatever the recipe calls for). Is that what you mean?

example:

Sugar syrup*
[1/2 cup sugar in 1/3 cup water - brought to a boil - boiled 3-5 minutes - cool until completely cold.]

4 oz unsalted butter, at room temperature
[1/2 cup beaten until light: sugar syrup is poured in while machine is beating]

* sugar syrup should be more than 1:1 ratio - 2:1 or 3:1 is better ..