How to teach a 3-year-old to write?

Before you go for teaching your 3-year-old child how to write, you must first ensure that he/she has reached the readiness point yet or not. I mean to suggest that children should be provided with enough opportunities for strengthening their finer muscle coordination.

Right from the beginning,  you can train them how to hold an object. 

The child should be engaged in different activities through play way methods. 

FINER MUSCLE COORDINATION:
If a child may not be able to master the skill of how to grasp an object or how to hold a pencil/crayon, it’s meaningless to forcibly teach him/her how to write.
Starting at about 2 years of age, children must be engaged in various indoor and outdoor activities which will help them strengthen their eye-hand coordination.

• Throwing and catching a soft ball
• Sand play
• Water play
• Clay modelling
• Fixing manipulative toys
• Color identification(first only the primary colors). Gradually move on to secondary colors.
• Shapes (circle, square, triangle, rectangle). Gradually go on adding many other shapes.
• Sizes: big/small, tall/short, long/short, fat/thin, thick/thin etc.
• Threading beads
• Tearing/folding/cutting paper
• Lacing and buttoning
• Free hand drawing and painting
• Fixing jigsaw puzzles 

Gradually, some pieces of chalk or crayon should be given to the children, side by side, they can be taught how to hold them correctly and then they can be encouraged to scribble on a slate, board or some paper.
All the above activities can be labelled/considered as PRE-WRITING SKILLS.
After they gain mastery over these skills, you can slowly proceed with teaching them how to trace different patterns, i.e. standing lines, sleeping lines, slanting lines with proper instructions to move from left to right, from right to left, from top to bottom or from bottom to top etc.

IDENTIFICATION OF ALPHABETS WITH PICTURES:

• Show big size alphabets for identifying and tracing them. 
• Ask children to copy and learn alphabets  and words. 

It's meaningless to force a child to write, unless he/she knows what is to be written.

 All these will help them to gradually start writing alphabets.
Though each child is unique, more or less,  children should be able to start writing at the age of three.