Migrate Active Directory to new server?
Solution 1:
The short answer is that you don't "migrate". What you do is join the new server to your domain as a member server, then dcpromo it selecting "additional Domain Controller in an Existing Domain", which will replicate all of your AD objects to it. Then you can gradually transfer the FSMO roles and other services across.
You'll want to update your AD schema before doing any of this, of course.
MS have some great technical articles on these items, so start by reading up on adprep >here<, dcpromo >here<, adding an additional DC >here< and decommissioning a DC >here<.
I'm going to recommend however that you don't decommission or demote the old server. You should always have a minimum of 2 DCs on a network, and it sounds like you only have one. This is not a good position to be in, as if you lose a single DC through hardware or software failure you will completely lose all network services that depend on AD until such a time as you get an emergency restore done. So keep the old one.
Solution 2:
You have a few simple main steps, of varying levels of difficulty. Promote the new server to a domain controller on the existing network. (Give AD some time to synch) Transfer all domain roles to new server. Transfer DNS & DHCP data to new server. Demote old server.
There are abundant walkthroughs for each step, but it's most important to complete & verify each one before moving to the next. Be sure you have backups & know what to restore where.