i am student want go to great wall from west beijing station how i go ? and where can rent the hote

Which section are u going to visit? Badaling or Mutianyu?

Badaling: take shuttle bus at West Train Station to Military Museum to take local subway line 1 to Fuxingmen, where transfer to MTR line 2 to Jishuitan Station. Then walk to Deshengmen to take bus n. 919 or 880 to the destination.

Mutianyu: use the way above to transfe to subway line 2 and you need to get off at Dongzhimen. Then walk to Dongzhimen Outer to take bus no. 867 to your destination.

As for the hotel, do you refer to that in either of the wall sections or city center?

i will arrive to west train station then after one day i will go to the wall and i want go to another places like forbidden city but i dont know how to go to this place
i want a cheap hotel nearby these places ? or nearby station?
please give the address of many beautiful places in BJ ?

Aside from the wall, you can visit Forbidden City (as you mentioned), Tiananmen Square, Summer Palace (At No. 19, Xinjian Gongmen Road, Haidian District), Old Summer Palace, Temple of Heaven, and Ming Tombs.

Well, from West Train Station, you can take the shuttle bus to Military Museum MTR Station, where take local subway line 1 to Tiananmen East or West, and then walk to Forbidden City.

For cheap hotel, it is suggested to find some chain ones, such as Home Inn, and Seven Day Inn. i am sure you will easily find the nearby branches.