Simply denying a cuckold sex and forbidding masturbation without permission are in itself a way of applying chastity, but as mentioned above, most cuckolds are so aroused by their submission and cuckoldry that they are frequently erect and eager to masturbate. Restraining his penis with a device or piercing, or combination of both, not only takes care of that, but deepens his sense of submission since it's very clear to him he no longer has any control of his own penis.
Reminding the cuckold that his penis is for the wife's pleasure, as her toy rather than as a male sexual organ, is an important element of cuckold training. The cuckold has to stop thinking of his penis as a source of pleasure for himself because when he has this idea, his attention will be focused on his penis instead of his wife and her lover(s). When he is used to being restrained and frustrated, he becomes accustomed to viewing his path to his own pleasure as being directly related to pleasing his wife and lover(s) in hopes of being released and rewarded.
What sort of interval is appropriate for each cuck varies from couple to couple as does most aspects of this lifestyle. In some cases I have only locked a cuckold's penis up as punishment for rubbing it without permission or cumming without permission. In other cases, I have required cucks to be locked up whenever out of direct supervision. In most cases when I'm fucking a wife in the cuck's presence, I prefer to him not locked so we can see and increase his excitement while at the same time denying him use of it. When in a more devious mood, I'll lock his penis up so we can watch it struggle in confinement while he watches.
Yes, forced chastity causes discomfort and at times mild pain. Enduring this is very much a part of your cuckold's submission. The discomfort of his penis trying to expand for you, the aching of his balls, are all gifts to you and your lover(s). For some couples it can also be seen as punishment for being unable to pleasure the wife and needing other men to take up his slack.
When keeping your cuck in chastity, keep in mind that he will need a little lubrication (baby oil works) at the spots where the cb will rub him. Also keep in mind that prolonged denial without prostate maintenance (draining) can be detrimental to your cucks health. Not being a doctor, I can't say how often he should either be allowed to spurt or manually drained (milked) to maintain his prostate health.
Milking, as it is termed, is a process where the cucks prostate is massaged manually but a dildo or fingers via his ass and his seminal fluid will drain from his penis with out any orgasm or penis-centric pleasure whatsoever. I have seen cucks milked daily, weekly and monthly - so it varies. I would suggest that at a minimum, a cuck should at least be milked weekly. Cucks sacrifice so much to serve their Mistress and Master and being masturbated in a ritual fashion or milked in a similar ritual is important for their psychological health as well and provides another substitute for physical intimacy since their penis has been retired as a sexual organ.
I typically prefer to have cucks masturbated rather than just milked, but again, these things vary with the needs of each couple. For those looking to explore the depths of submission, the more denial the better.
Enforced chastity can be achieved through the use of a device, piercing, or combination of both.