In college my reading teacher referred to phonics as clucking and spitting. My classmates and I thought that was pretty funny, and having little experience with phonics we did not realize how true that was. I have spent many years clucking and spitting since then, and I do have more experience with phonics.
There are many phonics programs and most people are very attached to whichever one taught their child(ren) to read. I heard Cheryl Lowe from Memoria Press share that people tend to keep trying different phonics programs with their kid, and the last one they try is their favorite. When in reality their child was ready. There is a great deal of truth in that. I am going to share a few suggestions and a few programs that I know of. The list is not all encompassing, and is just a place to start. If you have one that is working hold on to it and stay with it. For me it has been helpful to not rush out and buy them. Almost all of them are available at the public library. I have borrowed them to see if they were a good fit for my family. In my opinion a program has to work for your child and also has to be one that you are comfortable with. The following are some suggestions.
Alpha-Phonics: A Primer For Beginning Readers
This is my current favorite program. It is very easy to follow and is very systematic. I love the calligraphy print they use in the book. It is your systematic intensive phonics program. The front of the book has what your child reads and in the back they explain each lesson.
Phonics Pathways: Clear Steps to Easy Reading and Perfect Spelling
I have used this one as well. I do like this one and it was the final program that helped my daughter learn to read. Some people find this one hard to follow. Personally, I did not. I liked the long lists and it was helpful for my daughter from China. Definitely look at this one at the library before purchasing.
The Ordinary Parent's Guide to Teaching Reading
Well, I will admit that I have this one as well. I talked to Jessie Wise (the author) at a homeschooling convention, and she told me she wrote this for parents who have little or no experience in phonics. She shared that she likes Phonics Pathways, but wanted something easier for parents to use. This program also incorporates sight words nicely into the program. This is a scripted program.
Teach Your Child to Read in 100 Easy Lessons
I do not own this book, but know many people who like it. Cathy Duffy has a nice review here. It is not an expensive book and has a serious following. It is also a scripted program.
I believe magnetic letters are helpful with any of these programs. For some children moving around the letters and building the words helps them to connect to the text. For example, you are working on the word family "am." Below you have the letters "h, s, r, and p." Have the child move each letter up to "build" the word and then pronounce it. This is especially helpful with tactile kids.
This is my short list of what is out there. I know different curriculum programs like Memoria Press, ABEKA , The Phonics Museum (Veritas Press) , and Sonlight have phonics incorporated into their kindergarten programs. So there are many options.
My last thought on any phonics program you choose is to work on it consistently. It can be painful to sit with a child to which this is not an easy task. I would recommend taking 10-15 minutes every morning working on a phonics program with them. When the time is up stop, and move on to something else. I think short consistent times are better than longer inconsistent ones.