Hua Lamphong is the name of both railway station and MRT Subway station. They are located next to each other and you can walk between these two places.
Khao San Road is a short street where many backpackers choose to stay while visiting Bangkok. This street is full with bars, pubs, restaurants, and hostels.
Hua Lamphong connects with MRT Subway, while Khao San Road does not connect with any rapid train system. If you want to commute to Khao San Road from Hua LamPhong, here are my recommended options.
The easiest way to travel between these two places is to take taxi. The distance between Khao San Road and Hua LamPhong is about 5-6 kilometers. The taxi fare should be less than 100 baht. Well, please bear in mind that the fare depends on the traffic. If you come in group, I do recommend this option.
If you travel alone and want to save money, public bus could be your choice. The bus no. 53 runs from Hua Lamphong to Phra Arthit Road. Then, walk from Phra Arthit Road to Khao San Road; it takes around 10-minute walk.
Hope this helps