For your shoes,
With multicolored dresses, wear black shoes (if the colors on the dress are dark) or white if the colors on the dress are bright. Brown dresses will actually match red shoes while black dresses match well with shoes of any color.
In essence, your shoe, bag, dress and accessory shouldn’t be of a color. Utilize your neutral colors well. Neutrals are colors that work well with all other colors. They are impossible to clash. Examples of neutral colors are: black, white, grey, navy, brown (including camel, khaki, beige, etc). Navy and brown are not technically neutrals, but work so well with such a high number of colors, they are considered as such in the world of fashion.
Instead of neutrals, you can opt for metallic colors like silver and gold, plus a matching jewelry, and you are good to go!