If you are moving your website to a new host, but wondering about your SEO, then this video will give you an answer.

So it seems that there is nothing to worry about. As long as you are moving to a good host then the fact that you are changing your IP address should not make much difference for your ranking in search engines. If you are moving to a slower host however then that could make a difference.

The way to move hosts is the leave the old host up, while you change the dns to the new host that way the is limited interuption to the users.