Peek-a-boo is a game most babies love. Play it at odd moments in the day for a little fun.
Hold a piece of paper or cushion (or similar) in front of your face as you slowly catch your baby's attention by saying "peek-a " and show your face as you call "Boo"
play slowly at first
make sure you catch his eye
show your face from different sides
you can use a door, a chair . . .
This game is great for helping your baby to crawl and walk later when he's ready because there are "cross-patterned movements"
Sit your baby on your lap facing the room. Gently, slowly and evenly (constant) make movements with these rhymes:
I wave to daddy (one hand)
And kick a ball (opposite foot)
I wave to mummy (other hand)
Before I fall (opposite foot down)
See-saw, a handful of toes
Now I'll pick the others
I'll gather them in
To put in the bin
And I'll use my socks for covers
There will come a time when your baby wants to begin play. It takes a long time to learn to grip a toy, to hold it and to pass it from hand to hand. Give him the odd moment of help and encouragement:
Have a rattle, baby ring etc. ready.
Help him occasionally to move the rattle from side to side, use a simple beat
one-two (change sides) one-two
Make a fuss as though you are trying hard to pull the ring away with your hand
"What a tight hold! I can't get it away. What a strong baby!"
He is likely to enjoy the game and as his hand strengthens he is likely to enjoy it more.
note It's possible he will accept only one toy a favourite until he gets more confident.
Now if you want to soothe your baby while you wait and chat for a few minutes you can stroke his palm/fingers or put a rattle in his hand and shake his arm gently to help make a noise. A great change from the cuddle or a bounce.
For amusement between sleeps tuck some patterned paper or pictures into the sides of the pram or cradle.
Just looking & struggling to see is entertainment for a young baby.
Change the pictures when he stops staring and is indifferent.
In good weather place his pram under a tree branch gently swaying in the wind or even near the washing line, so he can watch the clothes gently sway.

There was a young farmer from Leeds
Who swallowed six packets of seeds
It soon came to pass
He was covered with grass
And couldn't sit down for the weeds