Hua Lamphong is the name of railway station and also MRT Subway station. The railway and subway are located close to each other, and you can walk between these two places.
Chinatown (Yaowarat) is one of the points of interest in Bangkok. It is the place where you can see Thai-Chinese Community and eat delicious street food.
Hua Lamphong connects with MRT Subway, while Chinatown (Yaowarat) does not connect with any rapid train system. If you want to commute to Chinatown (Yaowarat) from Hua LamPhong, here are my recommended options.
Actually it is not too far to walk from Hua Lamphong to Chinatown or vice versa. It takes around 15 minutes to walk (2-3 bus stops). If it is not a hot day, I recommend you to walk. Well, with this option, you should prepare a good street map.
There are a number of buses running from Hua Lamphong to Chinatown such as bus no. 4, 40, 529, and 542.
Since it is not far, taking taxi does not cost much. It should take around 35-50 baht depending on traffic.
Tuk Tuk is another great option. If you are in Bangkok, you should try taking Tuk Tuk at least once. The fare could be cheaper or more expensive than taking taxi depending on your bargain skill. However, I do not recommend this option if you go there during the day. Riding Tuk Tuk in a bad traffic and hot weather is not fun!