Meet everyone. This way you can get rid of those pesky ? marks on the social tab and get a little glimpse into what their character is like and what benefits you get from befriending them.

Focus on a few people at a time, particluarly the ones that you are interested in romancing. Chat to them every day and gift them something simple if need be, an extra point every day goes a long way. The My Time at Portia wiki has a lot of tips on which NPC likes what item.

Don't forget your friends! A developer has confirmed that your social points will decay if you do no interact with the person after a time limit.

Commissions are a nice little boost if you don't mind giving up some gols/ reputation. Portia's residents can put in commissions, usually easier ones, which reward the player with social points to their corresponding owner.

Don't get caught cheating! There's a jealousy system in place when you romance multiple characters. If you are out on a date with one and bump into another romanced character you will send both of them into a jealousy state, losing social points and not being able to interact with them (chat, gift, etc). You will have to gain their trust again by gifting or completing tasks or waiting 7 days.