How does Columbus "show off" what he has found/discovered in the New World after he has returned to Spain? -

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The way Columbus "show off" what he has found in the New World after he has returned to Spain was the following.

After the discovery of the American continent on October 12, 1492, Christopher Columbus returned to Spain on March 15, 1493. He went to report his findings to his sponsors, King Ferdinand de Aragón and Queen Isabella del Castille.

Columbus wrote a letter that made it to be translated into Latin to send a copy to the Vatican.

Columbus informed that he had taken possession of the new land in the name of the King and Queen of Spain, to honor and increment the kingdom of Spain. Columbus affirmed that he encountered no resistance from the island natives. Columbus added some descriptions about the geography of the land and the characteristics of the native people that inhabited the territory.

Finally, he ended up writing that the new territories could be easily conquered by the Spanish navy and that the native Indians were open to the Spanish religion and rule of the Kingdom of Spain.  

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