There are a total of 11 side investigations and they are split up into two groups.
The first is called 'The Fox Hunt' and it has you protecting the main games protagonist, Aiden Pearce. These investigations open up after completing the first mission in Act 2 called 'Bait'. Once you have completed 5 of these investigations a 6th bonus mission will unlock and has you hunting down bounty hunters who are after Aiden.
Below is a video guide if you are struggling with these investigation
The second type of investigation is called 'Council of the Daves'. These investigations open up after completing the second mission in Act 2 called 'Illusions'. Simply complete all 4 missions to unlock a 5th bonus mission which has you defending the Daves from enemy fixers. You can find Council of the Daves missions by going to the icons of a skull with white background on the map. Below is a video guide if you are struggling with these investigations.