When doing a site refresh we do something like this:
Audit Existing Site
1) Audit current sitemap & site architecture (urls, links, titles etc) to be sure we don't create any dead end links or stupidly remove any high performing pages, or that we redirect things appropriately (although we try to keep existing structure in place as much as possible to keep external bookmarks or links flowing in and maintain continuity of seo performance).
2) Audit the current website copy (WORDS are a huge part of web design which many new designers tend to overlook). Collect all the website copy together into buckets, or at least get a solid idea of what is where, so you can quickly analyze it and re-arrange, delete, or plan for new copy as needed.
Strategize New Site
3) Strategize the new site design (if you're working with clients you need to do this based on client's business goals). Build a new sitemap, figure out what the function of each page is, what copy we will need (look at the old copy and decide what to scrap and what to keep, and what new copy we need), figure out what additional assets we might need as far as photography, videos, or technology we might need, plan out any advanced functionality, conversion funnels, etc. etc.
Basically we create a blueprint of the new site and everythign we plan to do, while looking back at the old site and deciding what to keep and what to throw in the trash bin.
4) Create and/or gather all of the stuff we need to build the new site. Ie giving the client homework to create the copy we need, getting photography done, etc.
5) Finally the fun part. Design & Build the site.
*** Careful if you are messing with DNS & Hosting setup. You gotta know what you are doing here or you can mess up email systems and other behind the scenes tech.
Good luck man!