Every hydronic system is different, so there is no absolute correct answer when it comes to how often a dirt separator should be "blown down", however, we can make some general recommendations.
For new, relatively clean installations (with all new piping and heat emitters), you should be able to run the system for a week or two before an initial blow down. If the project is a retrofit, however, and has a lot of existing piping and old heat emitters, do an initial blow down within a day or two and carefully examine what comes out. If the system appears to be extremely dirty, repeat blow downs every few days, initially, to remove as much dirt as possible to protect any new equipment.
On smaller systems, purging a quart or two of fluid should be enough to completely clean out the separator. On larger systems, purging a few gallons should do it. Observe the fluid coming out; when it runs clear you can close the blow down valve. It's a good idea to collect the dirt in a white bucket and let it settle for a few minutes, then check it carefully. It is common to see solder balls, metal shavings, flux goobers, sand, dust, etc. A reddish/brown material is likely iron oxide (rust), a product of corrosion.
If you are using a magnetic dirt separator, such as the Caleffi DIRTMAG or DISCALDIRTMAG, you may also find magnetite, a highly magnetic and abrasive mineral, black in color. Magnetite laden water can appear gray, until it settles out, and is especially damaging to wetted moving parts such as pump and valve seals. It also builds up on heat exchangers which drastically reduces heat transfer efficiency and life expectancy.
Observe the water quality each time you do a blow down. When the fluid starts looking cleaner with each blow down, sample frequency can be reduced, eventually to 3 or 4 times per year. Again, every job is different and the maintenance staff can get a feel for how often it should be done. Systems with ongoing corrosion and dirt problems may require more frequent blow downs.
Regarding procedure, shutting down the pumps prior to blow down it not required, but, when the pumps are not running you can be sure all of the collected dirt in the separator will be purged and none will be carried through the separator by flowing water. If you have a magnetic dirt separator, remove the magnet before opening the purge valve. This will release any of the captured magnetic material so it can be purged. After closing the purge valve, simply re-attach the magnet.
One more thing, be sure the system fill valve is not isolated so the loss of pressure in the system (due to purging) will be made up. Click on the video link below; it's a very large retrofit project which, as the contractor discovered, had a BIG problem with magnetite!