To improve a first-grade student's reading skills at home, read with him, and point out common words such as "the," "to" and "and" to help him read more quickly. Explain punctuation marks and what makes a complete sentence. Help him build his vocabulary by adding verbs and nouns to his sentences or making corrections when necessary and explaining them.
Use rhymes to show word sounds and phonetics. Say an easy word to rhyme, and ask him to respond with other rhyming words to help him understand real words and the sounds they make. Go online, and find resources from teaching databases or digital education magazine that focus on reading and comprehension exercises. Some resources allow him to complete exercises online while others may need to be printed for use. Create flash cards for any word or grammar issues the student is having.
Read him short story books with illustrations, and ask him questions about what happened in the story. Use different types of books, from science-based themes to supernatural themes to themes on friendship so the vocabulary is varied and expansive. Start a dialogue with him about which stories are based in reality and which are imaginary. Explain synonyms, and ask him to use a synonym for words in the stories, and then add a few yourself that he may not know.