[verb ます-stem] + やがる
やがる goes on the ます-stem of a verb and shows contempt or anger toward the person doing it: "the bastard went and…", "how dare they…". It is very rough. You hear it in fiction from villains and angry characters, and it is never polite.
やがる itself is a godan verb: やがった, やがって, やがらない. The ます-stem stays as it is, so する becomes しやがる and くる来る becomes 来やがる.