If I want an espresso on Shabbat, what would be the best way for me to get a non-Jewish person to make it for me?
You cannot really have a non-Jew make you an espresso (which involves boiling water) on Shabbat.
This is considered benefiting from the labor of a non-Jew, which is not permitted.
Even if he boils water for himself, it is not permitted to enjoy the remaining boiling water, for fear that he will add for you (see Shulchan Aruch 325:11; Mishnah Berurah 66).
I believe that there are special espresso machines with a Shabbat module, but am not expert in this.