I believe that Sukhumvit is one of the popular areas to stay for many tourists while visiting Bangkok. Many visitors choose to stay in Sukhumvit area because there are many restaurants and pubs and it is also near BTS, the effective public transportation mode that will lead them to attractions in Bangkok.
And I believe that many of tourists land in Thailand at Suvarnabhumi Airport, the Bangkok main international airport. So, I will share you how to get from Suvarnabhumi Airport to Sukhumvit area.
Actually there are a number of buses and vans running from Suvarnabhumi Airport to several areas in Bangkok. But it might not convenient if you come with a big luggage, and also do not know the areas in Bangkok. So, here are the easy and convenient transportation modes I recommend.
Airport Rail Link + BTS Sky Train
With this option, you can avoid traffic congestion. Airport Rail Link connects Suvarnabhumi airport to Bangkok city center within 30 minutes or less, and it runs daily from 06.00 to midnight. Airport Rail Link connects BTS Sky train at Phaya Thai station. From there, you can take BTS to Sukhumvit areas such as Nana, Asok, and Thong Lor. The timetable and service route of Airport Rail Link can be found here, and you can read a guide to use BTS Sky Train here.
Taking taxi is a bit more expensive, but more convenient. Many taxis are available at the airport 24 hours. The fare depends on the travel distance and traffic congestion, and you have to pay a 50-baht surcharge. You can read how to calculate the taxi fare in Thailand here. Since Sukhumvit is a long road, it is quite difficult to tell you the exact taxi fare. Besides, it also depends on the congestion because the meter is increasing, when the taxi is standing still in traffic. Roughly, from Suvarnabhumi airport to Sukhumvit Road, you can expect to pay 200-500 baht plus tolls.
What you should know is currently all taxis in Bangkok are using meter, but sometimes a taxi driver might refuse to turn on the meter and offer you an expensive flat rate fare. I do recommend you to not go with that driver and try another one.
Hope this information helps. Enjoy traveling Bangkok!