The nearest airports to the Malverns are Birmingham International (BHX, about 45 miles north east via the M42 and M5) and Bristol International Airport (BRS, about 75 miles south west via the M5). Cardiff International Airport (CWL) is about 85 miles south west, and Heathrow (LHR) is about 125 miles south east via the M5 and M4.
Using public transport, it is possible to reach Malvern by train from Birmingham Airport by changing at Birmingham New Street. Bristol Airport can be reached by using a bus between Bristol and the airport, and then taking a train from Bristol Temple Meads / Bristol Parkway - via Gloucester or Swindon/Cheltenham. Heathrow can also be reached easily by train via Reading and the Heathrow RailAir Link bus, or from London Paddington and the Heathrow Express. Alternatively, National Express run daily coach services between Great Malvern and London.
Car hire is available at all the airports to enable you to drive to Malvern.
Birmingham Airport is particularly well served by Flybe, Monarch, Ryan Air, KLM, Air France, Lufthansa and Emirates (and United Airlines to New York). Bristol Airport is particularly well served by Easy Jet and Ryan Air. Heathrow of course is served by many international airlines including British Airways.