Begin by teaching your child the basics, such as letters and numbers. Make the letters of the alphabet familiar by cutting out pictures of well-known objects and gluing them onto a poster board with each object's beginning letter written over it. Spend time with your child naming an item and the letter it begins with. Sing the alphabet song several times a day. Children learn quickly with repetition.
To help your child to learn numbers, begin counting things during the day. Count out the grapes at snack time or the trees when outside. Show your child how to count his fingers and toes and practice this at least once a day.
Teach shapes by drawing them on index cards and showing your child each one while naming it. Find shapes in objects such as signs and furniture. Take walks and look for different shapes along the way. The same technique applies when teaching colors. Point out an object and tell your child what color it is. After a week of doing this, begin pointing to an object and asking your child to tell you what color it is.
Read to your child as much as possible. Hold a book up while reading so that she can see it clearly and point out interesting pictures. Choose silly books for fun times and books on subjects your child does not understand to help explain those subjects better. Point out words and letters as well as numbers and colors while reading.
Children love music in any form. There are many children's songs that use repetition to teach. Check your local library or bookstore for books of songs or for compact discs with songs on them.
There are many websites with printable teaching tools and online games. Sites such as HealthyMeals.nal.usda.gov and Time4Learning.com offer free tools to help your child to learn. They also offer online games that are geared to help preschoolers learn.
Other websites also offer many tips for parents on how to teach a preschooler most efficiently. Most sites also provide forums in which you can discuss ideas and concerns with other parents.