There comes a time in your kids life when they stop using nursing bottles, and they move on to using first sippy cups and then cups. Depending on the individual, this can come at the age of 3-4 months, 5-7 months, or even later. You should not get frustrated should your child not learn this early on as they have most likely learnt something else first. The development of the baby isn't always linear, and different things are learnt in a different order.
When you think it might be time to start thinking about using a cup instead of a bottle, you should look for BPA free sippy cups as they do not contain Bisphenol-A. This compound is potentially toxic, and with small children you should be especially careful not to expose them to these chemicals. A good time to start looking for sippy cups is when your kid starts to show signs of wanting to drink on their own. When you see them grasping for the bottle, or the cup that you are using, you know that they are interested and willing to try it out for themselves.
You don't want to start with a normal cup from the start as this would most likely be spilled all over the baby. This would result in a negative learning experience as they would get wet, and most likely the parents would be also frustrated as they now have to clean the area and change the clothes of the baby. Starting a with a learner cup that has a nipple shaped spout will be easy for the child to use and get started with drinking. Usually these cups also have small rubbery handles that are fitted for a child. This way even the smallest hands and tiny fingers can be wrapped around them.
Start with first showing the child how to use the sippy cup. Place it in their hands and slowly move it towards their mouth - soon they will realize that it is meant for drinking, and they will start using it on their own. When they get the hang of it, move away from all the bottles and start using these cups as the primary drinking device for the child. You might even slowly start using regular cups that are made of durable materials that won't break in case they are dropped.