I do a number of types of builds, so I'll go through what my process would be:
This could be a new layout for an existing website, a new modal design, or a re-usable part of the design that we might be using in more than one layout. Usually what's given to me will be a PSD (rare), an image-based mockup (common), a wireframe (very common), or sometimes just a verbal description (rare) or some combination of those. My job is to realize the needed design in HTML + CSS, and build the frontend part of it, adding any JavaScript interactivity I can, and then prepare it to be handed off to backend programmers for addition into a web app.
Here's how I would begin:
Depends on the complexity of the website.
If you're building a Single Page Application (SPA) or just a static, only a couple page, website then just get on with it.
However, if you're building something like facebook. Not social media platform, but just the multitude of components and moving parts that are there. Then it would be better to come up with a shared idea in the heads of the dev team and then work on a couple of use cases with the Minimum Viable Product (MVP) outlined, e.g. specific features etc. After that i'd throw together a couple of wireframes to confirm what it would look like then start building it - i.e. actually begin to code it.
Once you begin coding it's more of an iterative process as things will change, they always do. It doesn't mean you have to do everything all over again that I mentioned above but rather just acknowledge the new changes and their impact on complexity/time frames etc.
When you do finally start to code, try and have a rough timeline when features will be completed. Then just work off "sprints" or the "Agile" approach to development.
Hope this helped :)
Co-Founder, Founder, Entrepreneur & Problem Solver
Mev-Rael
Executive Product Leader & Mentor for High-End Influencers and Brands @ mevrael.com
Do first two steps for whole project at the beginning to get a full picture, then repeat all steps for each supreme system component/service. In case of large team with different tech stacks - each team (or just a team member in smaller teams) might be responsible for a single component of the system: auth, profile, news feed, settings, back-end, UI/front-end, testing, etc.
What you are asking for is called a Software Development Life-cycle (SDLC). Below I tried to provide short review of the whole process: