Hua Lamphong Railway Station is the main Railway Station in Bangkok. You can easily get the trains to other regions of Thailand from here. Hua Lamphong Railway station can easily be reached through MRT as it has a MRT station nearby.
Bangkok Suvarnbhumi airport to Hua Lamphong train station
Quickest way to reach Bangkok Hua Lamphong train station from Suvarnbhumi is to take the train. First, take the airport express train to Makkasan. A 5-10 minutes walk away from there is the the Petchaburi MRT station. From there the Petchaburi MRT station you will reach directly to Hualamphong station. Reference
Alternatively, you can take a taxi from Suvarnabhumi to Hualamphong train station. The taxi takes about 45 min.
Bangkok Suvambhumi airport to Bang Sue train station
In case you are tight on schedule or just about to miss your Bangkok train from Hualamphong, I will suggest you catch the same train from Bang Sue station. It takes about 15-20 for the train to reach Bang Sue from Hualamphong. To reach Bang Sure from Hualamphong, take the same Airport express train to Makkasan MRT and from there continue in the MRT to Bang Sue station.