If you didn't write your application with multi-tenant in mind from the start I would expect you would need to review almost every line of code that touches a database to make a transition like this.
In our code, the only DB-related piece of code which is aware of multi-tenant databases is the getDBConnection(accountId) function. Once you have the connection, you execute exact same SQL queries as before. The function is hidden deep inside the framework/infrastructure layer, so application code is completely unaware of it.
