How does Hamlet show Horatio that he feels there was haste in the Queen's second marriage? 

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Hamlet asks Horatio why he is in Elsinore, because he is a student at Wittenberg. Horatio replies that he has come to Hamlet's father's funeral, and Hamlet replies that he must really have come to see his mother's wedding. When Horatio observes that the two did, in fact occur in close proximity to each other, Hamlet engages in a morbid joke that illustrates his unhappiness with the situation:

Thrift, thrift, Horatio. The funeral baked meats 
Did coldly furnish forth the marriage tables.

Hamlet means that his mother remarried so quickly after his father's death that the leftovers from his father's funeral could still be served at his mother's wedding to his uncle. This, along with the bitter soliloquy a few lines earlier, in which he observes caustically that his mother went "with such dexterity to incestuous sheets" demonstrates his extreme displeasure with the whole unseemly affair.