what is the best way to update a database?

I have the next problem:

i have a database from app working just now, this app has new develops with many modifications in the database model (database B), now i have to upgrade the app getting the data from the database A and build the new model (database B)

What do you recommend to do the update? What is the main test of this case? Is there an application that facilitates the work? Wich is the best strategy to do somthing like that?

im working with sql server

Thank for your answers