As you may know, at Scarleteen we do not yet endorse suppressing menstruation/continuous birth control -- using a hormonal method of birth control in order to skip withdrawal bleeds/periods -- for women under 18, because there still is yet to be any study done or published with adolescent women to evaluate if it is safe or medically sound for those in that stage of physical development.
There is yet no available data concerning the long term effects of menstrual suppression on a woman's overall health, at any age. I should also mention that no studies have been published yet about the safety or efficacy of suppressing periods with the patch or vaginal ring.
However, there have been published and reviewed studies for women over 18 using oral contraceptives for suppression. Even though sample sizes have been relatively small (and to my understanding, without control groups of women not using BCPs), and they have been short-term studies, they have provided enough information to make clear that it is probably safe for most older women. Those studies have also shown clearly that suppressing periods/withdrawal bleeds properly does not reduce the effectiveness of birth control methods in preventing pregnancy. Some women (of all ages) also have health conditions where even if they suppress periods, it is potentially or surely safer/better for their health and quality of life not to have them or to have them infrequently.
But older women's bodies aren't the same as women who are in the thick of their sexual development, and not wanting to have your period because your boyfriend is wigged out by it isn't a health condition. Sexual development usually is not finished completely by 18; most women under 18 are still in that process, and some women's health experts have had particular concerns regarding breast and cervical cell development in this regard, concerns we feel are sound, especially with no study done with that population to review.
The Society for Menstrual Cycle research mentions their concerns about adolescent women and suppression in their position paper here, a statement in alignment with Scarleteen's current position. Until we have studies to look at about teen women and suppression, we're going to stick to our stance of not yet recommending this and instead suggesting that if this is something you want to do, you discuss it with your doctor.
Because we're not going to endorse this here yet, we don't have a sheet on how to do this here yet, either. I don't feel comfortable giving a how-to on something when we don't yet have any evidence it can be safe, particularly something that for most users here asking about it, isn't about managing otherwise untreatable pain with menses, but is fully elective and solely about convenience or the perception of convenience (for example, the idea you can't go dancing or swimming with a run-of-the-mill period, or can't have sex with a partner on a specific date you or they want to because you're menstruating and they'd be all grossed out). Again, if this is about pain or other issues with menstruation nothing seems to be helping, or about conditions like endometriosis or mood disorders, please consult with your doctor who can consider you as an individual and do their best to assess if suppression is safe for you.
However, we keep getting users who think suppression means they can manipulate hormonal methods in ways that would decrease the effectiveness of those methods in preventing pregnancy, and we have had heard some readers who have risked pregnancy when they did not want to take that risk or have become pregnant because of bungling attempts at suppression. Our users who want to avoid periods usually also want to avoid pregnancy.
Here's the deal: skipping the PLACEBO period (the non-active pill period, or the week-off period with the ring or patch) of methods that can be used to suppress periods will NOT decrease your method's effectiveness, and THAT is the way you can -- with our caveat about questions of safety -- try and skip/reschedule periods.
In other words, if someone wants to do this, she starts a pill pack (or ring or patch) as usual at Day 1, she takes NO LESS than 21 active pills (with any given pack), and then when she gets to the placebo pills/week, she moves right to the next pack of active pills, patch or ring without taking that week off. That may result in some mid-cycle spotting, but women doing this usually (but not always) will not have a full withdrawal bleed until the next time they take that placebo/inactive week again at the next scheduled time for one in the following month's pill pack. There are also a couple pill brands expressly designed without placebo pills in them every month as part of the regimen.
What you CANNOT do, if you want those methods to remain effective at preventing pregnancy, is interrupt the active pill cycle or skip ACTIVE pills (or rings or patches).
In order for your hormonal method to prevent pregnancy, you MUST always take the active pills or parts of a method exactly as directed. If you stop taking active pills, rings or patches mid-cycle, or start them late, those methods will no longer be fully effective and may NOT prevent pregnancy.
If you would like more information on suppression in general, including references to the studies with post-pubescent women, see this page from the ARHP: http://www.arhp.org/publications-and-resources/clinical-fact-sheets/menstrual-suppression
P.S. To be fully transparent, I personally have strong concerns about some of the attitudes about periods and menstrual suppression, and some of the unfounded claims about NOT suppressing, which I wrote about here. However, those opinions and feelings are separate from my concerns about safety and certainly separate from my addressing the issues of potentially and unintentionally risking unwanted pregnancy in attempts to manipulate periods.