Hafs (the way of recitation we are explaining) always reads the basmalah between two surahs. Meaning we read the basmalah before starting the next consecutive surah when reading the Qur’an, except between Al-Anfal and At-Tawbah.  There are four ways of completing a surah and continuing on reading to the next surah with the basmalah in between them.  Three of them are allowed, and one not allowed.

1.   Cutting off all from each other 

The reader finishes the surah, then stops and takes a breath, reads the basmalah, stops and takes a breath, then reads the beginning of the next surah. As in the following example:

2.   Joining all of them together 

The reader ends the surah, joining it with the appropriate vowels with the basmalah, continuing with the same breath the reader then joins the basmalah with the beginning of the next surah.  As in:
 

3.  Joining the basmalah with the beginning of the surah

In this way the reader finishes the last verse of the surah, stops and takes a breath, then reads the basmalah joining it in the same breath and proper vowels with the beginning of the next surah.  As in:           

4.        Not Allowed: Joining the basmalah with the end of the surah, then stopping, then starting the next surah.

This incorrect way leads the listener to imagine that the basmalah is the last aayah of the surah that was just finished. Here, the reader would join the end of the surah with the basmalah, then stops and takes a breath, then starts reading the next surah.  This is not allowed.