I am looking to graft some plum cherries and apricots need some advice on when the appropriate time to start.
Do I graft while the tree is still dormant or should I wait until there are leaves on the tree? If anyone here is knowledgable on the subject I would appreciate your assistance.

Not an expert but am about to do my first plum and pear grafting this year - scions are to be delivered this week.  For cleft grafting or whip and tongue grafting do it dormant.  For T-bud or chip grafting I think it is better to wait till the weather is warmer, the 'bark slips' whatever that means.

Ideally, the buds on the tree should just be starting to swell and the scionwood should be three or more weeks behind.

The three most important parts of the graft it's self is to ensure that the vascular cambium layer is aligned, not necessarily the outer layer of bark.  The graft union is as tight as you can make it without strangling the tree (ensure the a tight bond between host tree and scionwood cambium). And seal everything to prevent desiccation don't miss the tip of the scionwood if it has been cut. 

The advice above is good and the only thing I'd add is practice plenty before you work on your chosen tree. If you find several pieces of wood of similar diameter to the root stock/tree and scion practice your chosen grafting technique. This way you will not be wasting valuable resources.

When I started learning about grafting I went to several sites to learn more.  He is some I used.
http://pubs.cas.psu.edu/freepubs/pdfs/uj255.pdf
http://ufdc.ufl.edu/UF00067176/00001/1j
http://pods.dasnr.okstate.edu/docushare/dsweb/Get/Document-1040/F-6204web.pdf
It seems no one site had all the information, some had better diagrams than others, but I got pretty good knowledge to attempt a few cleft and whip and tongue grafts.  I plan to try some budding in the future.