Polegate is on the train line from London (Victoria Station) to Eastbourne and Hastings. The train line goes through London (Gatwick), making Gatwick the most convenient airport.
If you are flying in to London (Heathrow), there are regular coach services to Gatwick and this will be most convenient. (Cost: around £10, takes about an hour depending on traffic.)
For train times look here. Trains are twice an hour in working hours and take 44 mins from Gatwick, 1 hr 18 mins from London. There are also two trains an hour from Brighton to Polegate.
Allow three hours from Heathrow or other parts of London to Herstmonceux, and an hour and a half from Gatwick.
If you are driving, you'll need a good map. Herstmonceux is in the middle of the countryside and you will probably get lost.