Breakdown of Я считаю, что он прав.
он
he / it (for a masculine noun) / it (for a neuter noun)
что
that (conjunction)
прав
right, correct (as in "you are right")
считать
to count; to consider
Questions & Answers about Я считаю, что он прав.
Can I drop the word что like we drop 'that' in English ('I think he is right')?
No, in Russian you must always include что to connect the two parts of the sentence. Also, notice the comma before что. Russian grammar requires a comma before conjunctions that introduce a reported statement or indirect speech.
I learned that 'to think' is думать. Why does this sentence use считаю?
You can definitely say Я думаю, что он прав. The verb считать literally means 'to count,' but it is very commonly used to mean 'to consider' or 'to hold an opinion.' Using считаю sounds slightly more firm, like saying 'I believe' or 'I consider him to be right.'
Is прав a normal adjective? What if a woman is right?
Прав is a 'short-form' adjective used specifically to express that someone is correct. It must agree with the gender and number of the person you are talking about. If a woman is right, you would say она права, and for plural 'they are right', it is они правы.