The HSPT has remained stable in format, content, and level of difficulty compared to the SSAT which makes preparation easier. My teaching persona is coach, providing support and encouragement. We are a team--I'm ON their team. Nothing negative comes of this relationship. 
We begin with the Verbal Skills covering synonyms, antonyms, analogies, verbal classifications, and verbal logic. Part of my teaching style is vulnerability; i.e. I don't know it all. My students frequently outdo me in the verbal logic department much to their delight. :(  
I prepare them for 60 questions in 18 minutes. Yikes, you might say. 
The next section is Reading, where I show my stuff. I AM a librarian, after all. 62 questions in 25 minutes. Two parts, first is reading comprehension, and the second is vocabulary. We practice finding main ideas and vocabulary in context of the reading passage. Passages come from social studies, science, popular culture and current events. I teach how to:  

Focus on comprehension skills:
This section tests how well a student can analyze and interpret different types of texts, including informational, literary, and persuasive passages. 
 
Understand Vocabulary in context:
A significant portion of the reading comprehension section also involves understanding the meaning of words as they are used within the passage. 

Recognize question types:
Questions may ask about the main idea, supporting details, author's tone, inferences, comparisons, cause and effect relationships, and more. 
 
Language weighs in at 60 questions in 25 minutes. I teach my students how to find errors in punctuation, capitalization, word usage and arrangement of phrases and clauses in a sentence.