Just take it easy and you'll probably figure it out. You can raise their heart levels by just talking to them most days and doing requests. If you do give gifts, you can view their profiles and see how previous gifts have been received. The gifts be grouped by how much they liked the items, with a small symbol in the lower right corner if you've got that item with you. You will also have villagers telling you what someone else likes or dislikes, and that information will also make its way to that person's profile.
You'll likely end up viewing a bunch of heart events without even trying, but others require a bit of effort. At 2 hearts, you can enter a person's bedroom, or in the case of Leah and Elliot, their houses. Some events require that you enter a villager's house while they're in there, which might require a bit of schedule checking.