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Moving a website between top level domains is easy, getting search engines to follow is the trick. A few ideas for making the process more successful are:

1. As soon as you suspect you're going to do this, create a hosting account for the new domain and upload as many existing files to it (after necessarily modifying any internal links and sitemaps). My reasoning to this is having older file dates and maintaining close to 1:1 change ratio between domains/pages. Another trick if you use something like reseller hosting is to make sure to match the ip address if you have multiples in a pool.
1.1 Stop modifying the existing domain's pages - take a vacation, whatever.
2. Once you have control of the domain - TAKE YOUR TIME. Doing things thoroughly at this point can save allot of hair pulling, cursing and stomping on the floor. Test the site with attention to links that flow to the old domain. Sitemap programs and link checkers can have a good effect in this if you can scan a list of pages and focus on the extension to see if the old one shows up.
3. If you use Webmaster Tools, create a new account for then submit your "Change of Address" request. Getting a jump on this doesn't hurt, it can take a long time. Each change submission is good for 180 days presently and can be extended if necessary.
4. Forward/Redirect the old site to the new domain. For this step, there are a few points:
a. Use a clean .htaccess file, upload it or delete the existing one if you had ANY modifications in it.
b. If you use cPanel or a system like it, add a PERMANENT (301) "WILDCARD" redirect from ALL DOMAINS to the new one. (If there have others hosted, forward just the one in both www and without) Adding the redirect by hand is simple enough. (but don't guarantee anything on your server) I keep a copy of the original close to upload for any reason the new site isn't operating properly (you already have a change of address in place, don't sweat locations, make sure your site works).

Code:

RewriteEngine on
RewriteCond %{HTTP_HOST} ^.*$
RewriteRule ^/?$ "http\:\/\/www\.the-new-domain-name-here\.com\/" [R=301,L]

c. Test that the pages redirect properly. If you are using other things like forums or CMS in other directories, it's wise to check these for proper function now.
5. While you wait for the new site to be indexed, go to everyone who links to you and ask for the link to point at the new domain. If they won't or can't, be sure your redircts stay in place or any subsequent site will have backlinks when it starts.

To review:
Make a backup of your .htaccess file for when you move, any signs of trouble, send it back to the old server/hosting.
Any advance prep you can do like opening the new hosting account or setting up the server so you can upload files to age is great.
Make sure to do your change of address with sitemaps.
TEST IT TO DEATH - make sure every function works, especially if you use redirection for advertising.

In the end, any analytics you use should continue to operate normally, even Urchin or ga.js. Changing the name in your "Dashboard" may be useful for advertisers or your subusers.