Delicate. Because of the very odd (and I'd argue problematic) power dynamics in Eisenhower's cabinet, while Nixon was formally "in charge" during Eisenhower's incapacity in 1955, and again for a brief period when Eisenhower had a stroke in 1957, Sherman Adams and John Foster Dulles exercised the "real" power.

Since Nixon was Dulles's protege, this meant he could mostly rely on Dulles to guide and support him (indeed this is exactly what happened on the first NSC meeting held after Eisenhower's heart attack), but very much had to avoid being too assertive. Nixon and others stressed that Eisenhower's team was fully capable of running the show during the president's absence, and luckily no true crises broke out.

Adams was basically Eisenhower's gatekeeper, through whom all but a select few had to go if they wanted to see Eisenhower. There was apparently a common joke in Washington during Adam's time in power that went like this:

"Wouldn't it be awful if Eisenhower died and Nixon became President?"

"Of course, but wouldn't it be awful if Sherman Adams died and Eisenhower became President?"

So, more directly to your question. Nixon's role was to basically keep the NSC and department heads "in line" insofar as reminding them to keep all but the most important problems to themselves, not bother Eisenhower, and to go through Sherman Adams if they absolutely needed access to the president. Of course, since there were no genuine crises, and since Nixon was fairly respected by Charles Wilson (SecDef), this meant that while Nixon was definitely walking on eggshells, he also had important supporters. Having the Secretary of State and Secretary of Defense basically on your side, and knowing you can do little more than run meetings and gently remind people of their responsibilities gave him (Nixon) a fairly solid base. He was nonetheless praised by effectively the entire cabinet for how he handled himself, and even Eisenhower and Adams begrudgingly acknowledged he'd done well not to step on any toes yet managing to keep the machine running.

For more on this (and other Eisenhower-Nixon tensions) I'd recommend Jeffery Frank's "Ike and Dick", as it strikes a more realistic balance than the Malsberger or Gellman books on the same topic (though of course feel free to read and judge for yourself).