Best way from Southampton Central to Nats is to get on the train to Swanwick, should take 20 mins/half hour depending on train you get, then I would reccomend getting a taxi from there to Nats Whiteley, will cost around £6-8 and depending on traffic can take up to 25 mins so give your self plenty of time. You can walk from the station but its a bit of a mission and if you don't know the route then its probably not a good idea.
hope that helps.