Yes, you can start at home. As soon as your toddler develops an interest in drawing and coloring, you can explore the world of letters and numbers. Most commonly suggested age is 4 which is when your child will begin junior kindergarten but that is not to say you shouldn’t try to teach them earlier. Quite often they are very keen on wanting to learn to write their own name. At least their initial. So many products and activities a local bookstore to rely on to guide your child to learn to write basic letters and numbers. As toddler still struggle with precision and focus, it is key to always introduce this as a fun activity.
For example, try to make letters of their name or their initial using playdoh. 
Every single toddler loves to play with playdoh. But this way they will, while playing, learn to create a shape and eventually recognize the initial of their name. Children this age learn by repetition. It is repetition that forms the basis for learning, skill development, and accomplishment. Children will letters and eventually words by repeatedly seeing them written down. Similarly, with physical skills, mathematical concepts and social skills, your child will pick up ideas that are repeated and explained to them.
And as with everything, writing is one of those developmental milestones that varies greatly from child to child. Don’t stress out if your child isn’t even interested in writing. A lot depends on fine motor development. Just try to bring it up on various occasions and test their level of interest in wanting to participate. One day they will surprise you with their willingness and ability. And no-one can be more proud than a toddler who is showing off writing letters and numbers.