I'll be honest, many of the answers to this question here are far too simplistic and could be dangerous (for your site) because of the lack of information.

I've done about a dozen of these and each time it's complicated and something is missing. Here are the questions I've learned to ask.

Yes, 301 redirects are important between the old pages and the new, but digging deeper in that question you have to ask:

-Is just the domain changing, or are all of the URLs changing as well? For example are you going from oldsite.com/product-1 to newsite.com/product-1 OR are you going from oldsite.com/product-1 to newsite.com/products/shoes/product-name-32454?
-Is your whole website URL architecture changing? With whole categories of pages being added or removed?
-Are you moving your blog from a subdomain to your root domain or vice versa?
-Do you have ten pages on the old and new site, or tens of thousands? That will impact your method of redirects and how it affects site performance

Beyond 301 redirects, other things to consider:
-Can you isolate changes on your site into different stages? For example, just change the domain name and nothing else in this stage. In other stages you can change the design and content. Often times people want to go whizbang all at once and do everything.
-Are you switching platforms, such as a new CMS or Ecommerce platform? That changes a lot
-Are you dealing with parameters and filtering? Magento and other platforms create thousands and thousands of these URLs that you have to make a decision on
-Do you have a competent developer that will lead you, or do you need to triple check everything when it comes to SEO?
-Are you making sure all tracking codes make the leap between sites?
-Have you checked if the new platform has the same ability to edit important elements such as the title tag, meta description, URL, meta robots, rel=canonical, etc?
-Are you making sure that each page has it's own URL and you're not moving to a tab-based page view that will affect your page count? (Still matters)

This is just a sampling of some big important questions, and it's different for every project! Make sure to plan it better than you thought you'd need to, at least 30 days in advance.

Happy to answer any followup questions!