Take the Gatwick Express train service (a 30-minute journey, with trains every 15 minutes right from the airport) to Victoria station. £16.90 for a single and you can buy your ticket on the train at no extra charge.

Then catch the tube from Victoria station to your hotel (or take a cab, if you’re exhausted, jetlagged and carrying heavy luggage).
If you add a note to say which hotel you’re staying at, I can let you know which tube station is nearest. Or you can look it up for yourself on the excellent journey planner at London Transport’s site, here: http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2?language=en Just give Victoria as your starting point and type in the hotel’s postcode as your destination.

If you’ll be travelling by tube or bus at all while you’re staying, it’s worth buying an Oystercard. You pay a £3 refundable deposit and then just top it up with cash on a pay-as-you-travel basis. Oystercards are set up so they’ll always give you the cheapest fare across London Transport. You can buy one via the same link above.

Enjoy your stay here.
=D

Just to add to what’s already been said, I’d say take a ‘Southern’ train from Gatwick, instead of the Gatwick Express. It’s £6 cheaper (£10.90 for a Gatwick – Victoria single) and it’s only 5-10 minutes slower than the Gatwick Express. I’ve always taken the Southern (and Connex South Central as it was before) train whenever I’ve flown into Gatwick and found the service perfectly adequate. Trains every 15 minutes, most of them fast trains making only 2 or 3 stops before Victoria Station, £6 in my pocket… cushty!