When you interact with other Sims by socialising you will get closer to them and and form some sort of relationship. To instantly interact with another Sim tap the 3 dot icon in the lower left of the screen, above the clock and just above your character portrait. From there click the 'Relationships' option to bring up a screen that will display all of your current relationships in the game. If you then click the Sim you want to interact with more information will become available. This includes the Sims trait and an option in green, 'Socialize'. Click the 'Socialize' button and you can either instantly travel to their location or bring them to yours and activate a Relationship Event. When you then complete the requirements of these events you will be rewarded XP, Relationship Points with that person, and Sim Tickets. As your companionship level with a person increases new story options will will open up and lead you to new levels of friendship or romance.
When you are initially introduced to another Sim first impressions are important as this will decide how your relationship with that particular Sim will proceed. For example if you want a romantic outcome then flirting, dating, and giving presents are things you should aim for. Relationships are classified into 17 different categories which are listed below:
Arch-Nemeses
More Than Friends with Benefits
Soundtrack of Soul
Old Rivals
Raincheck, Please
BFFs Forever
A Missed Connection
Two Peas in an Odd Pod
Secret Crush
Geek Speak
Misery Loves Company
Tainted Love
Sports Buddies
Art Aficionados
Soulmates
Frenemies
The Fixer-Upper