What is the proper way to prevent water infiltration between exterior stairs and wall
When concrete is poured so that it will be in contact with a wood part of the building allowances should be employed so that moisture is  prevented from becoming trapped and is able to escape quickly. The wood wall that abuts to the concrete stairs should have been isolated with a vapor barrier. The most commonly and easiest to use would be 30 lb. roofing felt tacked along the stair/wall face. Metal flashing and self-sticking flashing would also prevent water from contacting the wall. An isolation or expansion joint would have helped any water that did find a way in to eventually evaporate. Repairing  the concrete  from contacting the studs is difficult. If there was any space between the surfaces a barrier could be retro-fitted. I'm not sure how feasible it would be to start cutting back the edge of the steps to create a space for repairing the wall? If you could that would enable the installation of treated lumber and water shields (flashing and felt). If not than all that can be done is to silicone caulk the wall/concrete joint, but water will still get in through the concrete by condensing.