Unlike some languages, English does not overtly denote its indirect objects by preceding them with the word to, so it is a little more challenging to locate them in sentences. However, this little word is understood. An indirect object is a noun or pronoun that comes after an action verb and before a direct object. Its purpose it to name the person or thing that something is given to or done for. (It is not the direct recepient of the verb's action.)
The direct object is a noun, pronoun, or group of words acting as a noun that receives the action of a transitive verb [transitive means action that directed to a thing or person].
So, in the sentence under question, the transitive verb gave is one that commonly takes both direct and indirect objects. The direct object is the noun praise.
Now, as this sentence is written, there is NO indirect object because the person to whom the public gives praise is the object of the preposition to (since the word to is overtly expressed, the noun is the object of a preposition and NOT an indirect object). In order to have an indirect object in this sentence, the sentence must be rewritten as follows:
- Literary critics gave Toni Morrison high praise for her first novel, The Bluest Eye, but the general public showed little interest.
In the boldface print "Toni Morrison" is the indirect object
In the italics, "praise" is the direct object