Tricky part with some website launches is that you will be moving the A record which is usually the website records such as www.yourdomain.com and potentially other records or CNAMES such as ftp.yourdomain.com  and it gets extra tricky when you need to change your MX records (for email) as well.  On occasion you are also changing DNS servers as well, and if you are getting super complex I guess you could be moving your domain name from Network Solutions to Godaddy as well.  This is the order in which you should do it.

Step one, you ideally a week before you want to actually launch your site and make the switch you want to get your DNS setup with a short TTL.  So having them on Godaddy is a great way for this to happen, their Time To Live is by default very short, so when you point an A record to another IP address it’s usually 15 minutes and your golden.  Network Solutions on the other hand, 15+hours.

I suggest having your DNS at GoDaddy whenever possible, I love their control panels. MyDomain.com is pretty good too but not as fast.
After you have moved your DNS server, do this days before you need to switch your other records, try not to do them all at the same time.  Move your DNS, then wait til that’s all good, then change your records.

When moving your A and MX records, one of the tricky things is there will be a time when some people will see the old website and others will see the new website.  For e-commerce sites this can be tough if you have people buying off both your sites at the same time.  Best thing to do is if you are on a fast DNS server and only expect 15 minutes or so of downtime, disable the checkout feature on your old site.  But up a message that says we are upgrading our server and we should be done by (this time).  Then once their DNS updates they’ll be on the new server and can checkout.

That’s the safest way to do it.
Just my notes as I have been doing a lot of these lately as we continue to grow and take on larger and larger projects.