Entertaining a baby and fun + tedious task as they are hyperactive. What I do is I sing songs with my daughter. I talk to her. I describe her how my day passes by, what I feel. The best is I sit with my baby at the window and show her vehicles, people, animals that pass by and describe to her the flying birds. I roam her around the house and show her things that are in the house.
Talk to him and sing to him. Babies want to see your face..,just narrate your day and make eye contact, sing songs, read books, do tummy time, walk outside, play in an activity center, play with toys like rattles and baby mirrors. Try and do sensory activities where baby is being introduced to different touches, sounds, and smells, toys with different textures, even something simple like taking a bath is a great sensory activity ]
Talk to your baby as much you can. While bathing talk to them, while making them sleep take to them, while they are breastfeeding talk to them, hold in your hands, kiss them several time and say you love them several times. Babies understand mothers language quickly since there brains are much more faster at this period. Talk while doing baby massage, laugh to them as they will respond to every reaction they make. While baby cry kiss them on their cheeks to make them comfort and let them know they are not lonely. Talk and kiss your baby as much you can so your bond will grow stronger day by day. Your baby will understand your language so dont worry.
I believe in taking the baby along with me for any chore outside the house (once they're over a month), because I think every such opportunity is sensory stimulation and change of scene for them. I also liked to hand them over to a y visiting relatives, especially grandparents so that they could observe and listen to people other than mom and dad. I'd also play music on a portable speaker.
I also liked the play gym I got for my younger one. she would play in it for about 10-15 mins at a stretch. also the rocker. I'd place th rocker in our balcony for her to get some light and look outside. would also take her to the pool
I would hold my baby and go walking in my house. We'd walk up to a picture and I would hold him so he was in front of it and you could see his little eyes scanning it. We'd pause like that for a few minutes and I'd move onto something else. Sounds weird but I read that this is a good way to stimulate a newborn so they see things and are thinking.
When I had my first, there was a lot of hype of black and white for babies and geographical patterns. They made mobiles out of this or there were cards you placed by baby for them to look at. Ever heard of this?