The effect of Horatio giving news of the ghost to Hamlet is that he is amazed and bothered (at least enough to find out more for himself). No doubt, Hamlet listens with rapt attention while Horatio tells his tale of seeing the ghost of Hamlet's late father the evening before. Hamlet asks Horatio question after question, finally ending with an inquiry about a further watch when Hamlet could join Horatio (including the determination that they would be armed "from top to toe"). However, it isn't until Hamlet is alone when he reveals his true feelings about the matter:
My father's spirit--in arms? All is not well. / I doubt some foul play. Would the night were come! / Till then sit still, my soul. Foul deeds will rise, / Though all earth o'erwhelm them, to men's eyes. (1.2.255-258)
With this second line arises an interesting (and well-known) controversy: does Hamlet speak of incest or does Hamlet speak of the possibility of the ghost's dishonesty? Either way, Hamlet has a bad feeling about the whole apparition.
Of course, the further effect of Horatio's revelation is that Hamlet himself goes on watch, sees his father's ghost, and hears that his father has, in fact, been murdered by Hamlet's uncle. Therefore, in a sense, Horatio's news puts the plot of Shakespeare's play into high action.