If you cannot buy programmes I would start with flashcards - choose the words that would most interest your children (and it will probably be a different word for the 3 year old than the 18 month old) Then show them the words you choose - and I would probably show both of them at the same time though you don't have to (but it will help you keep your sanity) Make sure you make the flashcards big enough - the younger the child the bigger it needs to be.
You do not have to teach the letters first because if you start with sight reading then they do not learn c-a-t says cat, they just see the word and say cat. Most children do eventually need some training in phonics and blending but I would not start that with the 18 month old until you have done a few words. You can try reading bear with your 3 year old as that will teach blending and is free (can't remember the site link but if you search on these forums you will find it or just google Reading Bear)
Personally I believe in a sight word and phonics based programme for reading especially with younger children. The more you teach them the easier it becomes for them and there are pros and cons to both methods so why not access the pros of both methods.
I started teaching my 4 year old to read when she was 1 year old by sticking two flashcards on the wall and telling her what they said. If I remember correctly the words I used were "Mummy" and "dog" both things she was naturally excited about. Within a week she could point to the word and say "doh" for dog and then point to the dog as he walked past so she had associated the written word with the spoken word and also the dog itself. I laminated the flashcards I made (in those days I was using contact paper as I did not yet have a laminator) and then I allowed her to play with teh flashcards in the bath and stick them on the tiles while reading them to her. She went through hundreds of flashcards before she was two and then I started putting them up as sentences and she would read them to me. I was also using Little Reader and Starfall (
www.starfall.com) By three she was reading beginner readers and I started phonics with her - she knew her letter sounds by 18 months so I just taught blending by blending everything for her - I never asked her to work it out, I just said c-a-t, cat for endless words and within two months she would give me the word if I just said the letters. I then moved on to The Ordinary Parents Guide to teaching reading and copied out the word lists into a lined manuscript book and taught her to blend the words by reading the letters herself. I only had 4 words to a page written very big and she would do two sets of 4 words per day with me teaching the phonics rule first and giving her a flashcard for the long vowel and digraphs (SH, TH, CH, OA, AI etc) She still has this collection of flashcards on her wall and if we come across a difficuly word when reading I ask her to find the flashcard for the sound she is sticking on and read it to me and then blend the word in the book - we only ever do this for one word per reading session as it slows the reading down. The rest I just sound out for her and she tells me what it says after I say the letters and digraphs/long vowel sounds.
We have not yet got through the whole of the Ordinary Parents guide to reading so are still doing that to make sure I cover all the necessary phonics rules (and I do not believe they are all necessary - that book is a bit overkill giving almost every exception - usually when these exceptions come up in a book I just tell her what it says and she remembers) She is reading at about a grade 3 level now though she does not have the stamina to read a whole book at this level so we do shared reading - she reads a sentence and I read a sentence. We have done this for quite a while and she is getting to the stage where she will finally grab the book out of my hands and read a few paragraphs herself so stamina must just come slowly.
At the same time as teaching all this I also used The Ladybird Key Words Reading Series with her - the reason I like this series (and you may find it works well for your 3 year old) is that to read the first book they only need to know 16 sight words - so you can teach your 3 year old those words first and then let her read both book 1a and 1b which means the child feels they have learnt a lot very fast and can read a real book by themselves. I would probably not use this series by itself, but it is a great way to start with sight words and they are the words most commonly used when reading English. Also the books are cheap to buy - do NOT buy the c series with a 3 year old - they are too young for the writing usually. My daughter has read to book 6a of that series and I have ordered the rest for her simply because she enjoys the characters and also for completeness sake - she is capable of reading most other books now though so if she gets sick of Peter and Jane we can always stop. I would advise that if using this series you buy up to book 5 - after that most kids can read a lot of other things and don't need to go further.
The one thing you need to know that is most important is this: everyone who tries to teach their child/baby to read succeeds provided they keep at it and are consistent. Every child also will have some issue with reading that will need to be addressed and you will need to find a solution for your child - for some it is reading left to right, some have issues moving from large print to small print, some have issues with stamina, some have issues with sounding out, some need more phonics instruction and some prefer sight words, some do not seem interested in books til you find one that excites them, some children resist reading unless you use a fun method to teach (and this can vary from child to child), some will purposely read words incorrectly (and I am sure they do this because it can get a response from the parent), some have issues moving to independent reading or silent reading and so on. Each of these issues needs to be addressed when it arises as they do not affect all children. So basically you cannot decide a reading pathway and just stick to it - you need to keep reevaluating and finding out what your child needs and when.
Nonetheless the place to start is either with letters or words. If you start with letters you need to move on to blending. If you start with words you need to make sure they can read the common words too (sight words) and then see if they need phonics when they start reading books. Good luck with your two children. And remember that at age 18 months and 3 years the concentration is not great - have "lessons" of only a few minutes about twice a day. My daughter is at a 3rd grade reding level and we still do no more than about 5-10 minutes of reading "lessons" - phonics and reading aloud per day. Consistency with short periods pays off more than long lessons done infrequently.
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