There are many ways in which one could find Gothic examples in the novel Frankenstein. (Some would argue that the novel is one which best matches the work of a Romantic author and not one of a Gothic author.)
First, many Gothic texts include an atmosphere which breeds mystery or suspense. Many times throughout the text Victor becomes suspenseful. The shutting of himself in his laboratory, the search for the monster on his own, and waking to find himself in a foreign land accused of murder.
Second, the Gothic text contains omens or prophecies. Victor dreams about murders and the deaths of those around him. One could look at these dreams as clues as to what is to come.
Third, Gothic texts include (perhaps most famously) aspects of the supernatural. Here, giving life to a long dead and decomposed pieced together man can be considered a supernatural element.
Fourth, many characters in Gothic texts experience heightened emotions- ones that boarder hysteria and terror. Victor experiences both of these emotions. When he discovers that his monster lives, Victor rushes from his flat terrified. It seems that every time Victor becomes suddenly emotionally charged, he gets seriously ill.