tedster - 1:28 pm on May 25, 2013 (gmt 0)
Years ago a new IP address sometimes (but rarely) caused troubles. I haven't heard of anything like that for years and years.
Here are some step-step instructions from Google's Matt Cutts in 2005. As far as I've ever heard, this approach worked back then and it still works now. Moving To A New Web Host [mattcutts.com]