Stand development

This is a rather special form of development where, in fact, it doesn’t happen much at all! 

The film develops very slowly. After pouring the dilute developer into the tank, and agitating for the initial 30 seconds constantly (which must always be carried out) some developers can be left standing with no agitation whatsoever.

I must be clear here... not many developers can be used this way. Try this with D-76 and it will just stop developing completely and your negatives will be ruined with bromide drag and other failings. However, work well and developers can just keep going and going, even at very low concentrations.
These ‘stand’ developers are usually very dilute indeed. An example would be Rodinal diluted at 1 part developer to 200 parts water (1:200) or even 1 part developer to 300 parts water (1:300) where the film will stand for an hour or more. Another good example is 510 Pyro that can be used to develop this way at 1:500 dilution. Now that's dilute!
Some two-bath developers require you to stand the film in the second bath for 3 or 4 minutes with no disturbance. Just remember that after either the initial agitation (as in the Rodinal example) or pouring in bath B (as in the two-bath formula) that you rap the tank two or three times to dislodge those bubbles sticking to the emulsion. 

One final word to the wise. Test this technique on some inconsequential photographs first. Don't ruin those great shots without getting used to it first.