1. Understand the business / talk to clients
2. Go through existing/similar systems to see how they work
3. Put together business requirements / spec doc. Usually a single doc.
4. Experiment & test (ie 3rd party APIs etc..)
5. Dig deeper into unknowns (ie. "I've never created that, lets think about the details")
6. Design draft database
7. Start writing code for major/most complex parts of the site
8. Fix/improve each of above as I move forward.
What else would you add?
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Ofcourse there's more things to but my main goal is to always get the fundamentals/main goal right and go from there.
This is usually the "core" of the system.