As your baby grows out of the newborn phase and officially becomes an "infant," their habits will develop right along with the size of their cheeks and their budding personality. In the first few months of life, your baby won't have much of a schedule when it comes to anything. But as they get a little bit older, their schedule should become a bit more predictable. Like every aspect of your baby's development, there are certain sleep milestones a baby should reach at 3 months that you'll want to keep an eye out for.
As you go through these milestones, keep in mind that every baby is different. Some will sleep through the night at 3 months old, while others won't until well beyond their first birthday. Your baby's sleep will be influenced by their temperament, feeding schedule, bedtime ritual, and more, so bear in mind that it's OK if your baby doesn't reach all of these milestones right away.
That said, it can help to have a bit of a "road map" for what to expect as your baby grows and develops. Even though your baby might not sleep exactly as you expected (or hoped,) these milestones can act as a guide when it comes to night time with your three month old.