How to get to Tianjin (by Train) from Beijing Zhong An Hotel

From Zhongan Hotel, I think you can easily walk to reach BJ Railway Station of subway line 2, so you can take that line to reach Xuanwumen Station where you can change to line 4 to reach the South Railway Station.
At South Railway Station, you can find bullet trains to reach TJ directly.

Thanks Alex,
My second part is after getting off in TJ how far is the cruise port and how much a Taxi would cost we are taking Voyager of the sea (Royal Carribeian) leaving on Oct.8th 2013

It is more than 50km between TJ Train Station and the cruise port, and the taxi fare shall be around CNY150. Well, I have a better idea for you:
Upon arrival at TJ Train Station, take a train to Tanggu. Then transfer to bus no. 102 or a taxi to the port. In this way, the taxi fare is within CNY20.

You can also take the train from BJ south to Tanggu. There are not as many trains that go the whole way, so if the wait is too long. Take the train to Tianjin then You can take the lightrail/subway or train to Tanggu