Though I often work within the established processes of the company I'm working for, when left to my own devices, I use the process documented below.
Customer and Stakeholder Interviews
Determine the wants and needs of both customers and the business.
Evaluate the competition’s strengths and weaknesses, and document features of competitors products.
Define and document the roles and characteristics of those who will be using the product.
Either as user stories or as a requirements document, define the tasks that users will want to accomplish with the product.
Knowing what users want to do segues into features that allow user to accomplish those tasks.
Process flows can be simple diagrams mapping out possible paths a user can take through a site or application. They can also map out detailed interactions, showing not screens but states of screens.
Define what UI elements are required for each screen or interaction, quickly working out UI problems and iterating through possible solutions.
With wireframes the hierarchy of elements on each screen is established and specifics of the interaction design take shape.
Depending on the level of detail required, prototypes can be basic click-throughs or simulate how the finished product will behave.