The external interrupt pins each have a circuit to clean up the interrupt signal and synchronize it to the 8086's clock. An input protection diode, inverters, and a two-stage latch. "Superbuffers" built from two transistors provide more current than regular NMOS buffers.
From there, external interrupts go to some logic that prioritizes the interrupts, decides when the system can handle them (usually at the end of an instruction), and signals the microcode to execute the appropriate interrupt code.