From about six months onwards, your baby will make massive advances physically. Brain cells make connections, which control and exercise muscles, from the top of the body downward. This is why walking doesn't start until the end of the first year.
From being able to sit with support, they'll gradually learn to sit unsupported. Then comes crawling and standing when held upright. Next, your baby will start pulling themselves up to a standing position. By 12 months they may take their first side-steps around the furniture, or even walk unaided. However, babies don't all go through every stage, some, for example, walk without ever crawling. Children who 'bottom-shuffle' - a kind of sitting crawl - go straight to walking.
At six months, a baby will move their head and eyes in every direction in order to absorb the whole of their exciting world. If you put a toy in front of them they will immediately stare and, almost simultaneously, stretch out their hands to grasp it. For your baby, touching and seeing are almost the same thing.
If given a toy, your baby will grasp it with her palm and fingers ('palmar grasp') and pass it from hand to hand, using their hands as tools, rather than toys in themselves. Your baby will also start using toys as tools, first banging them together and then doing things like dragging a cloth towards them so they can reach the toy lying on it. Gradually, your baby will be able to pass toys from hand to hand and from about 11 months they will use the more delicate 'pincer grip' on small objects. They will be less interested in putting toys in their mouth and will start to explore them with both hands instead.
By nine months your baby can put together sitting up and reaching and grasping with improved finger control - all of which makes for playing more complex, and longer lasting, games.