There is no typical project in web design and even less so in application development or SaaS but in broad terms the process is usually a concept and brief followed by investigative work that is then presented in the brief to the client. This could easily be presented along with user journeys and wire frames prior to the main development phase and then there's the ongoing maintenance of course.
The project overview diagram used here is usually reserved for larger enterprise level projects but any elements of this process can be applied to most projects.
An idea of how involved a typical project can be...
This is by no means a definitive approach.
I think the point I'm trying to get across here is that software, applications or websites by their very nature are dynamic so the process should be the same. The steps outlined above are not set in stone, nor are they fluid. Rather the approach should fit the project and not the other way around.
In case you were wondering
I enjoy taking either of these approaches...