I've really enjoyed some of the Montessori methods...information about these methods are all over the web. I ordered sandpaper letters in lowercase and had my two year old trace it with his finger and say the sound only. (He'd actually already learned the names of the letters but it is actually easier for them if they start with the short sound of the letters first.) We are currently working on this and doing 3 letters a week. He is almost 3 and has over half the alphabet memorized. I also have an alphabet chart in his bedroom and at bedtime we go through it several times a week playing little games with it. Either singing the alphabet song, guessing the sounds, saying words that start with the letter, etc. Sometimes he points to a letter and I sing the alphabet as fast as I can up to that letter. He really thinks that is funny. I've also taken this alphabet poster and taped it on our refrigerator and put up magnetized letters so he could match them up. Once that became a bore I took it down and moved it to his room. We also have a small magnetic board and I've put magnetic letters in a box that he's already learned the sound of and he pulls them out and puts them in groups, we say the sounds, etc. When he was very small he would have a whole bag of letters and he'd take one out at a time, show it to me and I would say the name and he'd put it on the magnetic board. We did this with capitals, but I sort of wish we would have started with lowercase, they are able to read much quicker with knowing lower case. Playing go fish with alphabet cards works great too.
Good luck, have fun.

Utilization of the Handwriting Without Tears writing program is a VERY good way to teach pre-writing skills and letter recognition.  It utilizes a multisensory approach (tactile, gross motor activities, visual, auditory) in the teaching of letter characteristics.  In fact, teaching the upper case letters first is recommended.  They are all the same size, can all be made with a combination of Big Lines, Little Lines, Big Curves, and Little Curves and have one of two possible starting points (Corner Starters or Center Starters--when utilizing small writing slates).  The lower case letters start at the middle line or the top line; some go below the bottom line and some start at the top line; there are several reversal possibilities with the lower case letters (p,q; b,d) where the upper case letters have no reversal counterparts.

One other suggestion would be to point to letters when singing the alphabet song--kind of like the math concept of 1:1 correspondence.  When you get to the part that goes LMNOP, I recommend pausing (el*em*en*oh*pee) so that it does not sound like one long letter named elemenohpee. At the end sing "W-X-Y-Z" not "W-X-Y and Z" because to many children it sounds like "W-X-Y-N-Z" which can be very confusing.  One child once asked me "How do you know which 'N' to use?"  Auditory discrimination is made a bit easier when one has a visual of what it is that they are to be discriminating.

Sit with her and make it seem like your singing and sing

Lots and lots of repetition over time.  Focus on a letter at a time.  Too many letters will overwhelm and not "stick" with a 3 year old.  Also, always teach the sound of the letter so that the child receive strong phonemic awareness for when she needs to learn to read.  Use a multisensory approach. Remember.... see it, say it, hear it and move with it.  After she masters a letter and sound, move on to the next letter but always review the previously learned letters or she will forget.  Because 3 yr olds don't have perfect fine motor skills yet, don't stress too much on the writing aspect.  Focus more on sound/symbol recognition.  Also remember to first teach all the consonants.  After she learns all the consonants you can slowly introduce the short vowel sounds.  This will enable her to begin blending sounds to form words.

Please use alot of play with your three year old.  "Play is the work of children".  A good book with lots of activities for learning the alphabet through play is Alphabet Soup: Stirring your Child's Interest in Letters.

you can either show her flashcards and tell her what letter they are or you can sing the alphabet song or let her watch seasme street

This is a quick way for them to learn say the letter example: "A" A.N.T "ant"ooo''   Thats SUPPOSED to be a picture of a ant
               '' '' ''
draw it out for them go threw all the letters and sing it at least 6 times every day with them if not improving get a toy that sings the abc's and have them listen to it b4 going to bed and twice during they day time
-parent_21

I'm a preschool teacher, for ages 1-4. We sing the alphabet everyday, until every child has it memorized. Then after they know the song, we show them a flash card a week, begining with the letter A. It may take a while, don't get frustraded with the child, because it will make her not want to learn.Try a letter a week and let her eat stuff that begins with that letter, this will help her learn the sound the letter makes. (Example, A-apple or B-banana).

find ways to sing it differently, or play alphabet games. The way i taught my daughters was when we were cleaning or together i would humm it and it sort of stuck in their heads and was even eager to learn the song. Make it more so fun than a chore.

well a way to teach your 3y old her alphabats is to sing to her sing it in a different way. if you see the alphabats are in a song it helps work with there mind a whole lot better.

I teach alphabets to  preschoolers aging from 2 &a1/2 to 3 &a1/2 yrs old by showing them an alphabet,pronounce its sound and ask them to pick as many letters as possible of that alphabet from among magnetic letters of different sizes and only the next immediate letter as  variation.[2 or 3 children at a time]I want to introduce any concept to a preschooler at always a win win situation.So that my intro will always be ridiculously simple,funny,and easy from an adult point of view.What I want is learning in a fun way.

The alphabet song is great. YouTube has a lot of good videos for kids, including several by me. See link.

say them one by one

I am a preschool teacher. I teach 3-4 years old. There are lots things you can do with your 3 years old child. I usually sing the abc song with them, however I always start to teach them phonetic sounds too. I have downloaded a phonic song to sing along everyday with them too. I only teach them the lower case and pick two contrast sounds for every new presentation. Story telling, nursery rhymes, flash cards, concrete toy object will be very good to enrich the vocabulary so that children can easily associate with the sound that we are learning... not only that to start with different kinds of phonic cards with two phonetics words, simple blends such is, in, at, then three phonetic words, sight words.. and in one year  or less the children will be able to read! Enjoy and have fun with your child!