We mostly played with my kids, and suddenly, they were reading! 🙂 It sounds like that’s just about what you are doing, too, and it seems to be working.
If she knows her letters and sounds, the next step is to start putting them together. There are several things you can do just as you go through your day that will help with this.
1. If you haven’t done this while teaching letter sounds, you can play word games about looking for words that start with a certain sound. Eg, I taught my kids that this was MMMMMMMMommy’s letter, D-D-D-Daddy’s letter, K-K-K-Katie’s letter, etc. Then a bit later, when riding in the car or making dinner and just needing something to do mentally, I would ask, “what other words can we think of that start with MMMMMMommy’s letter?” (It’s easier if the milk is sitting out on the counter, but we found lots of options.) This gives them the idea that words have distinct letters.
2. When I was reading to them, if the book had repeated words, I would give them a word to be “their” word whenever we came to it. So, eg, “Are You My Mother,” I would give them “Mother,” and every time it was there, I paused or pointed, and they would “read” their word. It helped them look at the words, and they did learn a few words by rote that way, but it was fun and I think helped build general word ability.
Putting letters together into words is actually very difficult for young kids. One thing I did was show them with my finger how I was reading the letters. Eg, I would say, running my finger along, “Oh, look! This says, “Ch-eeeee-rrrrr-iiiiiii-oooooo-ssssss, Cheerios!” We did that a lot, with things like stop signs, little signs we might see at the store, words on boxes at a meal, any simple word at a time when we had mental space for it. (I found out later that one major reading program teaches them to say it slowly, letter by letter, and then quickly. I was pretty much doing the same thing.) Because I was the one doing this, there was no pressure for them, but they were able to see what I was doing and get the idea of running the letters together.
Eventually, we got some of the little Mac books (which are pretty much twaddle, but my kids enjoyed them and they served their purpose 🙂 ), and they were able to sound these out.
I wasn’t really trying to teach my 3yos to read, but the older 2 were right at their 4th birthday when they were able to read, and the 3rd was 3 1/2. (Then the 4th was 6, just to keep me humble! 🙂 )