Difficulty: Moderately Challenging
Step1
Instruct your child to move her tongue so it is pointing at the roof of her mouth. Have her say "ahrr" to make an R sound. Do this yourself first and while the child watches. Repeat this process for a few days before moving on to the next step. She should be able to make the basic R sound with her tongue before moving on to words.
Step2
Mix the “ahrrr” sound with vowels. Ask the child to say “earrrr,” “orrrrr” and so on. Make sure the child’s mouth and lips are open. Speak these vowel combinations and ask the child to repeat. Repetition is key, but not so much that the child becomes annoyed and frustrated.
Step3
Combine two vowels together, even if these don’t make actual words, such as aro or ero. There doesn’t have to be a smooth transition between sounds, so it’s OK if the child pauses between the a, r and o. Eventually these will come together to form words.
Step4
Move on to words. A simple method is to point to pictures in a magazine or book with the letter R in it, such as car, rake or radiator.
Step5
Pair words together: Have her say "The car over there and the red car here" and other combinations. Say these phrases and ask the child to repeat them. Make flashcards for complete phrases, so a picture of a car represents “car over there.” Repeat this step with a varied list of common words.
Step6
Move on to more complicated words, not just words that start or end with an R, but words with an R in the middle, like "carrot."
Step7
Graduate to complete sentences. Work with the child on saying a chain of words all containing R.
Authority 
Comments
JimR said
on 6/10/2008 Treating and correcting /r/ articulation disorders is one of the most challenging tasks faced by speech-language pathologists. This article over-simplifies the challenge. One of the keys, that this article doesn't mention, is to be phonetically consistent. Good information on that can be found at: http://www.sayitright.org/R_Phonetic_Consistency.html
tgspch said
on 2/11/2008 I'm glad you had success with your daughter. But for most children, 3 or 4 years old is too young to even worry about their production of /r/. If you have a 3 or 4 year old child who only has difficulty producing the /r/ sound, you should just model good speech for them rather than pushing them to produce a sound that they are too young for. If your 3 or 4 year old child has difficulty with other speech sounds, then you should contact a speech-language pathologist to determine the presence or absence of a speech impairment.
Henry said
on 2/11/2008 I mention that you shouldn't start too young on this project. We did this with our 4-year-old daughter and it worked out perfectly, after only a few sessions. She was eager to correct the problem. For many children, such as my daughter, it's not a speech impediment but a case of slow development that can be corrected.
tgspch said
on 2/11/2008 As a speech-language pathologist with 25 years of experience, I would caution "Henry" against giving speech advice. Many children who have difficulty producing /r/ do indeed have a speech impairment. /r/ is one of the later developing sounds,and many children will not be able to produce it until after age 7. It is best for parents to model good speech instead of forcing their 3 or 4 year old child to correct themselves. Very young children are often not physically able to produce these sounds and will experience frustration when forced to attempt corrections at such an early age. If a parent is concerned about their childs speech production, they should contact a speech-language pathologist for a consultation.