As SurreyWeb says, we would need some further details in order to diagnose the cause of the problem such as the web site address as a minimum.
I've got a couple of questions for you:
1. How big a drop are we talking about, moving from page 1 to page 2 of search results? That could literally be 1 or 2 positions, going from 9 for a particular keyword to 11 (and so onto page 2) for instance.
2. Is this drop for 1 or 2 keywords or across a wider number? Are you regularly tracking the positions that the web site attains on Google?
3. How long has the web site been achieving lower positions on Google?
4. Have you made any other changes to the web site - redesigning any pages, changing any content on the page or title tags or anything like that?
5. Do you have Google verification in place and so have access to Google webmaster tools? Google webmaster tools gives you an indication of problems such as whether pages are unreachable, not found, etc.
6. Do you have a sitemap registered with Google - if you have access to Google webmaster tools and have submitted a sitemap you can see how many pages are indexed with Google.
7. Have you or the client been completing any SEO on the site or building (or buying) links?
8. Site performance is also a possibility - if the website is responding slower that it was before then it is possible that Google is starting to build this into the way it ranks sites.
9. Downtime - as SurreyWeb explained, any downtime during the move may have been noticed by Google.
10. Google Analytics - do you have Google Analytics in place? If so, are you able to determine what the lower positions have meant to the number of visitors arriving at the site?
My advice would be not to panic, collect some information together and complete an analysis of what may have happened first before you carry out any actions, as if you jump to a conclusion you can make the problem worse. Rankings do fluctuate and it is possible that the positions the site had before may bounce back in a week or two.
If the lower positions continue then further considered action can be taken. If you do not have Google verification or analytics in place then now would be a good time to implement them so this kind of analysis is more straightforward in the future.
