To see how many side quest you have completed go to your pip boy-data-stats-quest
In order for a quest to count it cant be a main story mission or a quest from a faction.
Quest that are given to you by people that aren't part of factions are counted as side quest.
To find them easily go to any of the main cities and talk to anyone with names. Some of them will give you quest. Sometimes while you are walking around you will find a new radio station, they can give you side quests.
Here is a list of quest for fallout 4 http://fallout.wikia.com/wiki/Fallout_4_quests
Look under side quest for a list of what quest you need.
Also some of those quest are miscellaneous which do not count.
These are the quest that i think are side quest. If you know any more or if i was wrong post it in the comments.Quick and Easy QuestShort Stories
- Vault 81, talk to KatyThe Devils Due
- dead body near Museum of Witchcraft / misc. obj. to investigate Museum of WitchcraftVault 81
- enter Vault 81In Sheep's Clothing
- Diamond City, after you complete the game fast travel to a place near Diamond City and walk there, when you enter go down the stairs and talk to the group of peopleOrder Up
- Drumlin Diner, talk to the WolfgangStory of the Century
- Diamond City, talk to PiperPainting the Town
- Diamond City, talk to AbbotThe Disappearing Act
- Diamond City, pick up Earl Sterling file in Nick Valentines Agency, might have to save Nick firstCambridge Polymer Labs
- Cambridge Polymer Labs, talk to MollyThe Silver Shroud
- listen to the Silver Shroud Radio near GoodneighborSpecial Delivery
- talk to Edward Deegan at Bunker Hill/ talk into intercom at Cabot HouseEmogene Takes a Lover
- complete Special DeliveryThe Secret of Cabot House
- complete Emogene Takes a LoverHole in the Wall
- Vault 81, give doctor blood, leave and come back to doctorConfidence Man
- Diamond City, talk to Travis, gaurd will give you a misc. obj. to talk to VadimLast Voyage of the U.S.S Constitution
- board the U.S.S ConstitutionCurtain Call
- listen to Trinity Radio near Trinity TowerThe Big Dig
- Goodneighbor, talk to Bobbi, she is at the end of an alleyway behind a doorTrouble Brewin'
- Goodneighbor, talk to Rufus RubinsHuman Error
- Covenant, talk to Honest DanVault 75
- enter Vault 75Long Time Coming
- Have Nick Valentine be your companion, After his third time asking to talk he will eventually give you the questDiamond City Blues
- Diamond City, Colonial Taphouse, watch Paul get beat up, talk to him around townOut in Left Field
- Diamond City, talk to Moe CroninThe Gilded Grasshopper
- Diamond City, pick up Marty Bullfinch file in Nick Valentines Agency, might have to save Nick firstPickman's Gift
- get misc. obj. to investigate Pickman's Gallery from any City / go to Pickman's GalleryPublic Knowledge
- Goodneighbor, talk to daisyEmergent Behavior
- have Curie be your follower and the first time she asks to talk you will get the quest - not sure if this counts