It looks like that ferry services from Tianjin to Incheon are on Thursdays and Sundays and services from Incheon to Tianjin are on Tuesdays and Fridays. You need check this. An economy ticket (one way) costs about ¥900. The highest class ticket for the same voyage about doubles the amount. There is a ¥30 port  construction fee per passenger.

Voyage lasts about 24 hours. 

The ferry service is operated by Jinchon. Their office in Tianjin: tel., (022) 23112843; address: No. 56 Changde Dao, Heping District, Tianjin. Their office in Tanggu: tel., 022-25719121; address: No. 36 Xingang Erlu, Yuanyang Hotel, Room 4025, Tanggu, Tianjin. They have a website at www.jinchon.cn; it is in Chinese and Korean but there does not seem to be an English version.

It is not a good idea to try to buy the ticket on the day you travel. It seems you can buy an open ticket but you need to confirm your berth 7 days in advance. If you need to change your travel date, you can ask the company to assign you a new date, but it has to be done 48 hours before the original departure time.

You can contact the Jinchon or travel agencies about purchasing tickets. In addition to the Jinchon offices given above, you can try to buy your ticket through from one of the following agencies: 

CTA Ticket Office: 010-65120507, 010-65120503; Guoji Fandian, 2nd Floor, No. 9, Jianguomennei Dajie, Beijing. 

Beijing CTA Ticket Office: 010-65158010, 010-65158564; No. 28 Jianguomenwai Dajie, Beijing.

Tianjin CTA Ticket Center: 022-28109123, 022-28109126; No. 22 Youyi Lu, Hexi District, Tianjin.

Tianjin Foreign Services Center (Tianjin Duiwai Fuwu Zhongxin): 022-28016005, 022-28016085, Guangyin Plaza, Youyi Bei Lu, Hexi District, Tianjin.

Tianjin Port Passenger Service Terminal (Tianjin Gang Keyun Zhan): 022-25706728, 022-25708344; Xingang Yihao Lu, Tanggu, Tianjin.