How should I use incorporate secondary, critical quotations into my own responses to literature?

It's important to approach the critics with a critical attitude. This means applying to the secondary material the same rigour and attention which you give to the primary material. You can do this in a few different ways. Look closely at the wording of the critical quotation: when Dr Johnson in the 18th century says that Shakespeare is a 'poet of nature', this does not merely mean that he was fond of wildlife - you need to understand the full work that the noun 'nature' is doing here. A critical attitude (such as the way that Romantics authors identified with Shakespearean characters) can tell you as much as the critic as the thing criticised. You can try the same approach with modern critics: ask yourself if the critical quotation is operating within a broader critical approach (such as feminist criticism or formalism) and then question how fitting that approach is for the literary work in hand.
Those are some good habits for approaching criticism, which will make much easier the second part of using criticism - actually incorporating the quotations into your essay. If you are careful to criticise the critics, it's likely that your opinions on them will be nuanced and substantiated: you won't blindly reject them, nor will you unquestioningly adopt them as your own perspective. You can now deploy critical opinions at key points in your essay: in your introduction, perhaps as a summary of a consensus from which you are about to depart, or perhaps to situate your own work within a wider way of reading, say Marxist criticism; in your main paragraphs, to highlight the complexity of your own reading - e.g. 'Goddard says that Hamlet is about the choice between art and violence; as my analysis of the quotation shows, this simple binary is continually challenged by the play'; or in a conclusion, especially if you want to indicate the plurality of a text - 'that two contradictory critical readings should claim for themselves the very same metaphor is fitting for a play which never allows us to resolve it's moral ambiguities'.