The quickest way will be a taxi
The best way depends on what you mean by best. The bus 100E goes from the airport to Deák Ferenc tér for 900 forints each way which is within walking distance of the IC and much cheaper than a taxi.
Even cheaper would be to take bus 200E to Kőbánya-Kispest where you can transfer to the metro replacement bus, but this may not qualify as 'best'. This trip would be included in a daily travelcard should you decide to get one.