I generally advise against this. The reason is simple. There often is little to no value in actually changing domain names.
Having said that, there are times where a domain name change is required.
The simplest way to do this is to set-up a blanket 301 redirect from your old domain to your new domain name. In the case where a page is removed, and you want to redirect to another page, then on the new server, set up a 301 redirect from the old page to the new page. If the page is removed entirely, then just let it 404. It is cleaner and far easier to do your redirects this way.
Using a 301 redirect will preserve some of the link juice and value of the old domain. It is said that a small percentage is lost with any 301 redirect. Keep this in mind.
Now please understand this forgotten issue.
It seems to always come about that the old domain will need to go. Whether this is the case or not, please do the following anyway. You will be happy you did.
Using 301 redirects should always be seen as a temporary solution. In this case, you will want to do several things. Every domain name should be able to stand on it's own. This means that you will need to build TrustRank, SiteRank, and see how many of the old backlinks you can change to point to the new domain. You will need to build a new backlink profile for your new domain that matches or exceeds the backlink profile for your old domain. Your new domain will be at a disadvantage being new. For example, domain age is a TrustRank metric that has to be regained over time. However, most if not all other metrics can be regained. You will want to work on this along with the backlink profile so that you are not hamstrung by the old domain.
The old domain will continue to benefit your new domain only as long as the old domain remains and the 301 redirects remain. If this is broken, then the value is lost. Keep in mind that stuff happens and even temporary glitches can effect the new site rank very quickly which will take time to recover. This is where you will be happy that you worked on the backlink profile of the new site and the various trust metrics for your new site.
Once done, you will at least have some options not everyone enjoys. You can remove the old domain safely if you do your work well. Better yet, you should be able to make the new site perform better than the old site and therefor would be better off removing the old domain. This is a powerful option.