Nordkette sits in Tirol (Innsbruck), Austria, at 860–2256 m. Getting there mostly comes down to altitude and whether you're driving or flying in — here's the practical part.
With 860–2256 m of elevation, the access road often requires winter or M+S-rated tyres, and snow chains can be mandatory on heavy snow days. Check road conditions before you drive up and build in extra time for the last few kilometres of mountain road.
The reference airport is Innsbruck Airport (Kranebitten) (INN), in Innsbruck — from there, it's 15 min by cable car from the city centre, no car needed.
Most resorts have paid parking right by the lifts and free options a bit further out with a shuttle. Arriving early on busy days (weekends, holiday weeks) is the difference between parking right at the slopes or walking quite a bit further.