Take road number 61 or 57 and aim for Pułtusk. From there join road number 57 to Biskupiec, before heading via road 596 to Bęsia. After that follow signs to Reszel. Alternatively, from Biskupiec reach Reszel via road 590 which passes through the town of Leginy.
If you steadfastly refuse to get into a car, and that’s not an unreasonable stance to take considering the kamikaze nature of the roads, then simply take a train to Olsztyn Główny before bussing it into Reszel.