Hi Leon,
Welcome. Most people who measure runout of loaded rounds have either the RCBS Case Master Gauging Tool ($64.99) or the Sinclair Concentricity Gauge ($91.50/w Dial Idicator) ($74.90 w/out Dial Indicator) or versions thereof.
Just lay the loaded round in the bullet guide (RCBS) or on the ball-bearings (Sinclair) and slowly rotate the round while the dial indicator is touching the bullet. I usually let the indicator tip touch the bullet about the ogive. You can, however, also use these nifty tools to check runout of cases. For fired cases this would show the trueness and concentricity of your rifles chamber or for re-sized cases would show the same values of you re-sizing die.
I made the one that I use by looking at the Case Master in the RCBS shooting catalog. I used Delron for the base mounting plate and also for the bullet/case guides. Works just fine. My cousin made one using ball bearings and it too works just fine. Hope this helps, as I know of no other way to check for runout, other than rolling the loaded round across a desk top (gotta have a quick eye for that). Good luck. Johnny K.