You can just simply interact with him! Make silly faces, laugh and smile at him. He will get excited, kick his feet and smile back at you. Sometimes babies of this age enjoy tickling or having their feet played with. You can also put brightly colored toys in front of him to encourage him to reach for them.
At this age, your baby loves to hear the sound of your voice! Sing songs to him, talk to him, tell him everything you are doing. Count slowly to 5 on your fingers. Pick him up and dance around the house with him while singing. Have fun!
There isn't really a whole lot you can do with a three month old, as far as physical activities. Some good ideas are listening to music, or singing to them. Clapping your hands, or clapping their hands. This is about the time they start enjoying their mobile on their crib.
Three month olds will be sleeping most of the time, when they are alert you can sing to them, go on walks, go to the mall. Sit on the floor, make sure you have them on their tummy at least three times a day for 20 minutes so that they can develope strength in their neck.
Babies this young can sometimes be over stimulated quickly. The most important activity though would be just talking to your baby, as you are going through you daily activities talking and singing to your child helps them learn.
Reading to your child is always a great idea. Look at the books together and point out the objects. 3 month old also enjoy being in the standing position. They love holding things that makes sounds like a rattle. Make funny faces and funny sounds. Talk, laugh, sing and play.