You will be getting to know your baby better and better each day and should start having a routine going. You should hopefully by now be able to get some rest.

Motor Skills

Your baby’s neck is always getting stronger and you should be seeing either very little head wobbles or none. When your baby is laying on their tummy, they should have enough upper strength to support their head and chest with their arms and be able to kick out their legs. Tummy time is important as it helps them with their co-ordination motor skills needed for movement and their muscles. It's best to start small with the amount of time your baby has for tummy time so start with 5 minutes then work the time up till you get to either around 15 minutes or 30 minutes. Remember to watch your baby still as they aren’t stronger enough to hold themselves for long so you might have to rescue them. You might notice now that your baby’s hands can open and shut, swipe at things in front of them (normally colorful things), start to grab at toys and put things straight into their mouths.

Communication

You might have noticed your baby taking more in now as their vision is improving, they are starting to have control over the movement in their eyes and that they are focusing on faces more. Your baby should be able to recognize the sound of your voice now and they now understand some tones with which they will laugh or cry. You will be noticing your baby smiling a lot more now and trying to imitate noises. Your baby’s crying should have calmed down now as they know different ways to communicate but if for any reason your child is still crying a lot then you might want to make an appointment with your doctor or health visitor.

Sleep

As your baby should be consuming more milk now, they should start sleeping better and for longer at night and should roughly be sleeping for 5-6 hours and should hopefully be having lesser feeds at night or none which means they should be alert more in the day. You might find that your baby only has about 3 naps in the day although it doesn’t mean all babies will sleeping through the night or only napping about 3 times in the day as every baby is different. If your baby is waking up in the night then maybe wait about 30 seconds before heading into them as sometimes baby might cry for a few seconds then fall back to sleep whereas if you go to baby straight away you might wake them up more and they then might not learn to fall asleep by themselves. If you do need to go into your baby’s room at night as they aren’t falling back to sleep then make sure you only do what’s necessary i.e. Changing nappy, feeding and winding and try it to do it with minimal lighting then put baby straight back to bed.

Feeding

Now your baby is 3 months old you might be feeding them frequent but more ounces if you feed your baby when they want and how much they want they will be more content and sleep better.

Development

Helping with hand and eye co-ordination. You can help your baby by putting these toys in front of them and letting them grab them themself.

Back and neck muscles. By letting your baby have tummy time you will be helping them to strengthen their muscles.

Vision. By showing your baby colors, patterns, books, comforters, baby mobiles, and activity mats you can help develop their vision.

Talking. Your baby will by now respond to you like they are talking so to help them talk back even though you don’t know what they are saying they are trying to communicate.

Source: https://www.ameliawilliam.com/blogs/amelia-william-baby-clothes-blog/3rd-month-with-baby