What's the best, most reliable, quickest,and least complicated way to get from Narita to Haneda? We have less than 4 hours between flights!

www.narita-airport.or.jp/airport_e/
Use this website to find ground transportation between Narita and Haneda airports

Still need advice on changing airports in Tokyo. The website gives me all the options, but I want to know which option is BEST. The limousine bus? The train? Private taxi? We have three hourse between flights. Is that enough time? Please help!

It may just be doable. It takes a minimum of 90 minutes by train (most reliable way) to get from NRT to HND. Any other option that includes road transport is subject to unforeseen delays. Keisei runs through trains between two airports called Airport Rapid, or just one change at Aoto, and delays are rare. It will take a minimum of 30 min to get through passport control and customs, and up to 20 min waiting for the right train. Add them together and you are at Haneda train station around 100 min min before departure. The minimum check-in time for domestic flight is only 20 min. Should you miss your flight (perhaps because of late arrival of your inbound flight), I've found Japanese airlines to be quite helpful in re-booking on next flight.

Thank you so much for the information. Do I need to book the train in advance?

No, you can't and don't have to. It's a normal commuter train that uses Toei Asakusa subway line and Keikyu line to get to Haneda. You normally have to change once, at Aoto, for a thru train to Haneda. Every train from Narita, except Skyliner, stops at Aoto. You can buy a thru ticket at Narita.