How does Shakespeare use soliloquy to inform us about Richard's plots, as well as to reveal his character in Act 1 scenes 1, 2 and 3?

Soliloquy is used to keep the audience informed as to what particular characters are thinking and, in this case, plotting.

In all three scenes, Richard is shown to be 'mis'hapen' but very articulate. In scene 1 Richard tells the audience that he is more suited to war than peace because of his deformity and in times of 'romance' is 'determined to prove a villain'. So here the audience's introduction to Richard's cruel, almost abhorrent, personality is formed.

In scene 2 he carries this further by convincing Anne, whose husband and father in law he has had a hand in killing, to accept a ring from him. His soliloquy here reveals his gloating nature. He is very sure of himself and makes sure the audience hears about his plans and schemes as well as how clever he is in achieving them.

By scene 3, not only has has he proven himself to be articulate and scheming, but also murderous as he plots to have Clarence killed. These traits are taken to the ultimate degree throughout the rest of the play.