A good place to start is with the child's name. Ask her to say words that begin with the same sound as her name. For example, if her name is Mary, coax her to say words like "mom", "mop" and "mouse." Then move on to other names or words that the child knows, perhaps the names of her family or friends. Ask her to once again say words that begin with the same sound.
Alliteration cards can be purchased or you can make you own. At the top of each card is an image, something familiar to a child. Across the bottom are three different images of familiar things, only one of which begins with the same sound as the image at the top. Ask the child to look at the card and say the word for each image. Then ask her to point to the image that begins with the same sound as the one on top. Provide positive feedback whenever the answer is correct.
Develop silly phrases where each word in the phrase begins with the same sound. Use phrases that conjure up a specific image. For example, "Polly Parrot put peanuts on the pink piano." Write the phrase on a sheet of paper and give it to the child. Say the words, pointing to each word. Ask the child to say the phrase out loud and then draw a picture of it. Ask the child to draw a circle around the letters for the sound being repeated. You can also ask the child to come up with her own silly alliteration phrases and help her write them out.
Present the child with an image of an animal and help her write the name of the animal on a sheet of paper. For example, if you show her a pig, help her write the word "pig" on a sheet of paper. Then write the word "the" in front of the word "Pig" and underline the "P." Ask her to help name the animal with a nice name that starts with the same sound. For example, the child might decide on "Perry the Pig."