How do you deal with people who change their minds all the time and want something changed in mid-project?

This is a very difficult question. Our processes have been designed around “XP: Extreme Programming” which works towards being able to handle just this situation. We spent close to 50% of the time allocated to any project on design, architecture, prototyping and thorough documentation before we write a line of code. We do understand that no client can be hundred percent sure about their requirements at the start of the project. To counter this we first develop the prototype of the entire application (Minus the backend code) and get that signed off screen by screen for the entire application. Usually it has been seen that majority of gaps get filled up at this phase and the chances of missing out important functionality as well as making changes mid-project are reduced. In addition we recommend a iterative process for managing changes. Our methodology makes this possible and practical.