Here is my almost sure-fire reading program, developed with my sisters while teaching my younger brother (who wasn't supposed to be able to read at all), then honed on my six kids and several little ones that I babysat. The ages ranged from three to seven, and took anywhere from a few months to a few years.
I've assumed that you read to your child quite frequently: if not, it's never too late to start! Try to find simple books that interest your child. Ones with good artwork may also delight you!
Be careful of the books that you buy to read to your child. There is little that can discourage the love of reading more than a parent who resents reading aloud, and there are few things that can make a parent more resentful of reading than being practically forced to read a badly-written, nasty book over and over for months!! (I have 'accidentally lost' a few particularly vile ones in my time!!) You can be a bit less picky with library books, since they will have to go back anyway...and the time can come as quickly as you need it to!
Also be careful of books that talk down to your child. They can understand much more than they can say, and books with a large vocabulary can be challenging and fun. It's very enjoyable to hear your little one say, "I implore you to exert yourself!" after being read Peter Rabbit...
When your child becomes comfortable and happy with books, and is not quite so inclined to tear them, it's time to learn to read. The outline below is just my way of doing it. There are many different approaches to teaching reading, but this one is simple and cheap, and it works quite well with many kids. Of course, you should investigate other ways, because it may not fit you or your child. It's based on phonics, and uses a bit of sight reading later on.
First, get magnetic letters for your refrigerator, upper case because they're harder to mix up. Put them on for a few days, then start telling the child a few sounds a day...
be sure to use short vowel sounds:
a as in hat
e as in get
i as in pig
o as in hot
u as in hug
and hard consonants:
c as in cat
g as in get
After she's learned a fair number of letters, show her how to combine them to make simple words:
...and so on. Be careful not to let her get into the habit of guessing from the first letter. That's a very hard habit to break later on. One way to discourage that is to give her several words that start with the same letter. Then make simple sentences, like "The fat cat sat on the mat." Throw in family names that she can learn by sight and sound. Add more simple words as you add sounds. Then begin to add words that have long vowel sounds. like cape and date, explaining a bit about the magic of Silent E.
If your schedule permits, make your child a Photo book. I got this idea long ago from a very good book called Anything School Can Do, You Can Do Better . Use folded construction paper, and glue family photos to each page. Write very simple sentences at or just above you child's current reading level, in upper case. Be sure to include family names and details, even if they're not quite phonetic. Your child will learn them by sight and phonics because they're important. These are excellent to put in your child's baby book, to be looked at and treasured years later...even with the chocolate stains and rips from overeager hands!
Then it's time for co-reading, that is, sharing the task. Let the child read the words that she can, while you help out on the harder ones. Pick books with few words on each page, and very large print. Your child will begin to make the transition from upper case only to lower case as needed rather quickly, if he hasn't already picked it up by asking and osmosis.
Try writing words like 'Skip' and 'Hop' on slips of paper, and let the child read the word and then do the activity. Or write a phrase like 'can of corn' on a slip and give it to the child to read and fetch from the pantry. Encourage reading the words she can handle on cereal boxes, signs, newspapers, computers, etc.
An excellent online site for beginning readers is Starfall. This is free, and it has several levels of stories, games and activities. It also gives the kids something to do online like the big kids!
After that, it's time to step back a bit and become a book supplier. Listen to your child read, and make sure she's taking the time to read accurately, but let her have private reading time also. Continue nightly bedtime stories (even young teens often still like them!), and maybe even let your young one stay up a bit later than usual to read in bed!
Truth is, nearly all kids will learn to read by the time they're ten with little or no help. It's thought to be wired into our brains.