I will be in London Wednesday thru Sunday. Staying near Bayswater Station. Will be going to see much of London in zone 1. Probably take the Tube 4-6 times each day. Need transportation from LHR to Bayswater and am also taking trips to Windsor and Hampton CP. Do I need the 7 day Oyster or should I go with something else? What exactly do I need and how do I ask for that?

An emphatic yes for an oyster card! The convenience is worth the purchase fee. You will move through London with no hassle. The card work in all zones and on all types of transportation (tube, rail, bus). You simply swipe the card at the turnstiles as you enter and exit. The correct amount is deducted for your trip.
I bought mine through the internet before I flew over, but I'm sure you can buy them in underground stations. For the amount of travel you anticipate, I'd charge the card with 30 pounds to start with. If you use that up (a panel on the turnstile warns you to recharge), you go to a vending machine to top the card up.

Assuming you're traveling alone...

When you are at the Heathrow tube station, go to the window and ask for an Oyster card (£5 deposit) with a 7-day zones 1-2 travelcard loaded on it (cost is £27.60) You also need to tell the window agent you wish to travel to London from LHR. Because LHR is in zone 6, you'd need to add another £5 or so to the Oyster card so that the machine can deduct the additional fare that's not covered by your zone 1-2 travelcard.
http://www.tfl.gov.uk/tickets/19799.aspx

Never pay cash-per-ride: they want you to prepay, either through pay-as-you-go or a travelcard.

If you're on your own (and therefore won't benefit from the national rail companies' 2for1 offers, for which you'd need to buy one of their tickets, which could include a London travelcard on paper rather than electronics):

for five days, it might save you a bit to get a 7-day travelcard (for zones 1/2), with a bit extra for the add-ons to Heathrow and Hampton Court, but there isn't a lot of difference between that and the maximum you'd be likely to pay using pay-as-you-go. For Windsor, you'd need to buy a national rail ticket as an entirely separate operation.

In your position I would get a 7 day travelcard for zones 1 and 2 loaded onto your oyster card. To get to hampton court, you could either by a separate ticket or load some pre-pay onto your car to cover the extension. Windsor is not on the oyster card system so needs a paper ticket in any case.

Are you travelling alone? If so then a 7 day Zone 1-2 Travelcard plus £15 PAYG cash loaded onto an Oystercard will be the best option as that will cover your travel to / from LHR & Hampton Court as well as travel within central London

If "I" is "we" then come back as there's other options that can save you LOTS of money