How soon can someone start training after an angiogram?

Depends on results. The answer depends on the results of the angiogram, the site of catheter insertion (either femoral or radial artery) and the type of training .Many centers, such as mine, are inserting the catheter into the radial artery in the wrist which does not require any post angiogram attention. A patient whose angiogram was negative and had this method used, could return to all activities the next day.
Depends on site. Of arterial access (radial vs femoral) and what findings or intervention were performed. Talk to your physician who performed it but generally in 4 days if no complications. I'm assuming this was a cardiac angiogram.