Have you printed the free high frequency word flashcards with phonics rules on the back I shared in a previous post? You may find them helpful. Make some blank flashcards to write more high frequency words you want your beginning reader to practice. Be sure to visit this link for more teaching ideas to use with the flashcards.
I've shown ways to introduce some VC words and CVC words. V stands for vowel and C stands consonant. If a child is comfortable reading words with short vowel sounds, it is time to try to add all the VC and CVC words to your pile of flashcards to practice. Add a few at a time and remind your reader to be ready for a short vowel sound.
VC - and, at, in, is, it, on, up
VCV - can, red, yes, did, big, this, will, with, not, but, fun, run
Here are some books I recommend for a child reading short vowel words. These are the most interesting phonics books I've found. If you have other suggestions for short vowel stories, please share in a comment.
Starfall Learn to Read
I'm also recommending any Brand New Readers or any Scholastic Readers Level 1 to include stories with picture clues, some rhyming, and some repeated language ideal for beginning readers. I believe children should have a combination of phonics and easy reader books. Phonics books provide a child an opportunity to practice sounding out words but should not be the only books he or she is given to read.
If you want to learn about and practice some simple phonics, try out this site.