The best places to find information are often birth, marriage and death registers and census returns.

You can search the national index births, marriages and deaths for England and Wales 1837 onwards for free at Central Library: Pre 1915 birth, marriage and death certificates are now available to order at Archives+.  Details of how to order are available here. Census Returns are compiled every 10 years.  The first useful census was in 1841.  They contain information about everyone in a household on the night the census was taken.  The last census to be released to the public is 1911.  They are available on-line for free at Central Library.  
The 1851 census books for Manchester were badly damaged by flooding while in storage.
Before civil registration in England began in 1837, key events in a person’s life were typically recorded by the church rather than the state.  Parish records are the best source of vital record information in England before the nineteenth century and remain an important source thereafter.  Details of the parish records held at Central Library are available here Manchester & Lancashire Family History Society undertook a 14 year project which concluded in 2005 with the publication of transcripts of the legible entries.  Despite the damage, details of some 82% of the 217,717 persons whom the statisticians had counted have been recovered.