Southampton Airport Parkway train station is closest station to the University and is also directly adjecent to Southampton Airport. From Gatwick Airport, it is best to take the train via Clapham Junction (approx. 1h 40m). From Heathrow Airport it is easiest to take a direct coach (approx. 1 hr) with National Express. Alternatively take a RailAir coach to either Woking or Reading and then catch the train to Southampton Airport parkway, or take the London Underground to Victoria train station and catch the train from there (both approx. 2hr).
Train times can be found at http://www.nationalrail.co.uk/
From the Southampton Airport Parkway station (and directly outside Southampton Airport), the Unilink U1 bus goes directly to Highfield Campus. There are is also a taxi rank - it is a 10 minute drive to Highfield Campus.