The chances are, if you're coming to Qatar, you will arrive at Doha at Hamad International Airport, which opened after months of delays in May 2014. The airport is located around 20 km from Doha Corniche, so it's quite a quick journey to most hotels. At present, US pre-clearance is not available in Doha, but this is on the cards.
Unlike in Oman, taxis are metered and pretty affordable - a taxi from the airport to the Grand Hyatt for example should cost 35-40 QAR ($11, €9, £7). Blacklane Limousines is available in Qatar but prices are roughly double that of a taxi (if you are a new user, you can use code 4NMXMSYB for a discount). Although there are plans for a rail system, there is currently no metro or train service available in Qatar. Public buses are available but we would recommend using taxis for ease and comfort.