If you are asking what changes have occurred in the php language that you will need to make to bring your code up to current php standards, there are migration sections in the php.net documentation that list the removed, backward incompatible, and deprecated features.
If you are asking about current programming practices to use, it would be more direct if you posted your code somewhere for it to be examined, either in the forum or on github.
For database implementation code, yes, use the much simpler and more consistent PDO extension, use prepared queries when supplying external/unknown data to the sql query statement, use implicit binding (supply an array of data to the execute method call), and use exceptions for database statement (connection, query, prepare, and execute) errors and in most cases let php catch and handle the exception, where it will use its error related settings to control what happens with the actual error information (database errors will ‘automatically’ get displayed/logged the same as php errors.) When making the connection using PDO, set emulated prepared queries to false, set the error mode to exceptions, and set the default fetch mode to assoc. Doing these things will result in the simplest implementation code and simplest sql query-build syntax. You will be able to eliminate a lot of database related code, rather than to convert it.