Budapest airport to downtown hotel

TAXI ...... something less than $30. Follow the black line from baggage claim to the outside FoTaxi kiosk. You will be to your hotel in less than 40 minutes.

Or you can book for the private transfer company.
You can check them on tripadvisor, or other sites from Hungary.

There's also an express bus if you're pinching pennies (as I do). Bus 100E makes three stops: Kalvin ter M, Astoria M, and Deak Ferenc ter. I think those M's refer to Metro stations, but I am not sure. Bus 100E requires a special ticket costing 900 forints, or less than $4.

If you are just with carry on luggage I would say the bus, then transfer to the Metro for the final leg. For a couple you will save maybe $20 and most hotels can be gotten to in less than an hour and a fifteen minute including the final walk. Just depends on which hotel.

There is the shuttle service too. Maybe save you $15 per coupe and could be less than an hour if you are one of the first drops, maybe 1.5 hours if you are last.

Private driver like http://www.silverwings.hu is excellent and comfortable. About $40.00

Taxi or driver, less than 45 minutes to most hotels.

I might try the new airport express bus when I visit in May; then again, the ease of a taxi is always tempting. Time of arrival might make a difference, too--if you're a first time visitor to Budapest or arriving at night a taxi is probably best.

The combination of the regular airport bus and metro is 1/2 the price of the new express bus, and just as easy. A discounted connection ticket is sold.

The direct Airport bus is 900ft
The 100 Bus is 530 including 1 transfer (which you will most likely need)

So the difference is 370 ft or about $150
With a regular ticket, in the event you dont need a transfer, the 100 Bus is 300 ft, a difference of 600 ft. Or not quite $2.50.

The best way is by taxi (or the private car service mentioned by James). The trip won't take long, you won't be in a crowded bus, and you'll be delivered to your hotel's front door.

The most economical way is by bus. However, it will most likely be crowded, depending on how much luggage you have it can be a challenge, and you'll have to navigate to your hotel.