Use letter sounds rather than names...I taught DD1 to read before school. (I thought they would be taught 'sight reading' rather than phonics and I wanted her to learn using phonics -turns out they did use phonics...)
I agree with back learning common letters first
play I-spy using letter sounds
have things like (lower case) alphabet bricks around -make sure if they have picture for letters they make the simple and right sound - so 'g' for gate - not g for giraffe. Nothing beginning with 'th' - also try and avoid words like 'f' for 'fr'og ( you can hear the difference if you say it out loud -we generally tend to pronounce two consonants - eg 'fr' - together... )
Draw simple pictures of things that start with the same sound.
I agree with 'at' being a good place to start - make a list of words - cat mat,
rat, bat, hat draw pictures of them on one side of cards with what they are written underneath and have the first letter on the other side then have a and t cards together - let them choose the right letter and they can turn it over and see if they got it right. (you can do sat and pat but they are harder to draw!!) - go through the alphabet and do the same with 'nonsense' words - sound out say d -a--t and say that isn't a real word - what about 'gat' - is that a real word?
I supported a child with dyslexia learning to read and we spent ages talking about sounds, trying to blend etc -with no success - one day I asked if they knew why and what we were doing - they didn't. So I explained that letters make sounds and you put the sounds together to make words etc - they completely got it. After being unable to spell or read even cat - they came in the next day saying I can spell 'dragon' (and they could - except thy put 'en' on the end!) After they flew - so if they are struggling tell them what you are doing.
Once you have 'at' words move onto 'an' , 'ad' 'ap' -do a few then change the vowel - so 'it' 'in' 'id' 'ip' etc
Also at the start say all words don't follow simple rules -but lots do. (so they don't get confused why it is 'gate' and not gat-e -that pesky magic e!!)
Personally I hate jolly phonics - the idea is some children learn better in different ways - so the actions etc can help some children to remember the sounds - once you work out the way your child learns - eg by just looking or if they find tracing over a letter on paper with their finger -or if they need the actions - stick with that. I said DD1 could read (had a reading age of 8 at age 5) - she knew her letter sounds. A couple of times she got upset because she couldn't remember the action for the letter - which is kind of missing the point!
DD2 I deliberately didn't teach to read (like I said I knew they did phonics and I don't think it did DD1 any favours as she was the only one and also she was convinced she couldn't do maths because she had to try -whereas she didn't for reading). Both DD2 and a friend when asked what letter they had learned that day said 'm' - they hadn't - they had learned 'i' - but they both thought 'm' for mouse -not 'i' for 'inky' mouse...
Finally lots of reading with them and books available...let them tell stories just using pictures -so they get the idea of how a book works.