There r several ways to do the job like, In-place upgrading which requires sp1and enterprise to enterprise / datacentre to datacenter but only standard to both edition. Another way is to go from 2003 DC to 2008 DC and is restructuring AD. This help to move all resources from one DC to a new fresh DC. One more is transitioning, but hope u did not mean that. It means adding 2008 DC to existing AD. However u can take any one. See here from step by step guide for ur idea and concepts.
2008 is actually running on x64 and i believe your 2003 is running on x86.
you can get another idea from here too
you actually can read from here too