Read to your child from the time they are born. Let them see you read books for yourself as well. Set up a regular daily reading time during which all family members sit together and read to each other or enjoy their own books. This establishes with the young child that reading is an enjoyable activity that all ages can do.
Show the child simple words in the books you read together. Make simple letter-sound connections the 3-year-old can understand - for example, letter S sounds like a hiss, which is the sound a snake makes; the snake looks like letter S and starts with that letter. Focus on two or three letters at a time and make it a daily game, one day concentrating on words starting with C and D, another day with letters L and M, and so on.
Purchase or make basic flash cards with one picture and one letter per card. Start with one card for each letter of the alphabet, using one- or two-syllable words the child already knows. Show the child letter B and a picture of a bear and letter D and a picture of a dog, for example. Repeat these connections periodically throughout the day until the child can identify the letter sound at the beginning of these words without your help.
Teach the child simple word families. This demonstrates that different sounds correspond to different words. Show the child a list of words - cat, hat, rat, bat, mat, sat - and teach the beginning consonant for each, showing it with a corresponding picture. Learning a list of these related words is fairly simple for most children but will give them a strong sense of accomplishment at having mastered "lots" of new words.
Encourage your child to "read" to you. Let them start with familiar stories; even though they're primarily just retelling a story, they begin to think they're actually reading it. Use easy-to-read books, like the rhyming Dr. Seuss books, to encourage them to begin sounding out the words themselves. Repetition is a key factor in learning to read, but do vary the books periodically, so your child doesn't just memorize the sounds that match each page.
Encourage your child to practice her reading in casual settings as you both go about your daily routines. Keep magnetic letters on your refrigerator so she can make words while you're fixing her lunch. Ask her to sound out the names of foods in the grocery store, words on traffic signs as you drive to day care or the instructions to her favorite game. Linking reading to everyday activities and praising her progress will help establish for her that reading is a natural, enjoyable and rewarding activity.