Why is Richard shown to be more than a one-dimensional evil man in Richard III?Please just some main areas to know which direction I need to go, and some depth.
I am going to assume that your question is really "How is Richard shown to be more..." rather than "Why." We can find examples in the text to support "how" something is shown, but "why" is a trickier question that involves a lot of supposition. Here are some places to look for more to Richard than his evil schemes.
In Act I, scene ii, he shows a nice seductive quality that adds dimension to his character in his wooing of Lady Anne. He woos her with flattery, saying that he fought for love of her:
Your beauty was the cause of that effect
Your beauty, which did haunt my sleep
To undertake the death of all the world,
So I might lie one hour in your sweet bosom.
It is the sort of line a character like Romeo might utter.
The other moment that stands out for me is the fear and vulnerability he shows in Act V, scene iii after his is visited by the ghosts:
Have mercy, Jesu! Soft, I did but dream.
O coward conscience, how dost thou afflict me!
The lights burn blue. It is now dead midnight.
Cold fearful drops stand on my trembling flesh.
What do I fear? Myself? There's none else by...
And the speech goes on in self-examination that belies the sort of unthinking murderer, blind to everything but his own ambition, that Richard has been up to this point.
These two moments stand out most strongly to me as departures from Richard's evil deeds and schemes.
I'm going to answer this as why and not how.
Shakespeare simply does this to create a moral conflict for the audience and so makes the play more compelling for the audience. Richard is a character driven by evil, and such receives the end he deserves. However, the audience also sympathises with him and feels somewhat sad at his death.
If Richard had been a one dimensional character, the multiple reactions that he evokes from the audience wouldn't be possible, and as such the audience would be less involved in the play. Much of the impact the play makes is because of Richard's multi-faceted character. Hence taking away from Richard's character would also take away from the play.