The most important way is for Catholic families and parishes to be prayerful and orthodox. Both prayer and orthodoxy are equally necessary; for even as spirituality without orthodoxy is gnosis, orthodoxy without spirituality is pharisaism. But when both are present in sufficient measure, the people understand what a great and special vocation the priesthood is and are willing to transmit that attitude to the young men they influence. Dioceses where that process occurs, such as Omaha, St. Louis, and Denver, get ample vocations. The last of those three is even building a bigger seminary. In the solid and growing Diocese of Charlotte, plans to build a seminary from scratch are well advanced.
There are other ways too, but I lack time to get into more detail about them. Here I'd rather focus people's attention on the biggest obstacle to the spread of such ways: the extent to which American cultural values shape the outlook of most lay Catholics themselves.
I just came across a blog called Roman Catholic Vocations, where today's post offers a vignette about the young author's process of discerning a priestly vocation. What most struck me was not the post, however, but the first and, so far, the only comment. It is by "A Simple Sinner," who often comments here too. He wrote:
A dozen years ago before I left for seminary, the most common comment I got from my suburban neighbors when I told them my plans (you know, people who are members of suburban parishes, put their 2.1 kids through the parish grade school because it was a better "private school" and bragged about being buddies with priests...) Don't do that! You'll find a girlfriend!" The message being clear - I wasn't such an unattractive loser that I couldn't do far better than becoming a priest! I later came to suspect that a young man taking a step to be a sign of contradistinction to all that we hold dear in the US - sex, money, fame - is a challenge that bothers people who themselves may feel guilty how NOT seriously they take their own faith. Sure they will put $25 in the collection plate on the Saturday nights they do go to Mass... But give up their granit-counter-top homes, his & hers SUVS, birth control, sex, money? Now that is just plain crazy!
SS is right about one thing: the default assumption is that the priesthood is for losers, so that a young man who could get a girlfriend and a good job doesn't belong in the priesthood. That problem was fully apparent during the aftermath of Vatican II. As a young man in the 70s, one who could and did get girlfriends and could have had a remunerative career if he'd actually been interested in something that remunerates, my interest in the priesthood drew mostly the reaction that SS describes. I'm still interested in the priesthood and, when I express that interest, still draw the same reaction (even before the perennial child-support issue comes up, which it doesn't always). But I don't think SS is quite right to "suspect" that many of the scoffers secretly feel guilty. If I thought they did, I wouldn't be in the least disturbed; for somebody's guilty conscience is a sign that they know, at some level, that they're guilty of something. The real problem is that, among most Catholics, the necessary formation of conscience isn't even taking place.
They don't think of the priesthood as a noble vocation from God at all. That is partly because nobody has told them—at least not in any convincing way—and partly because they have no idea that to adopt sacrificial service willingly as a lifestyle, for love of God and neighbor, is to be divinized. But they don't see as much mostly because all the cultural icons that suffuse their environment send the opposite message. As some wag once asked: "Why does the Devil have all the best tunes?"—a question much more apposite now, if only given the state of Catholic liturgy, than it was a century ago. The gods and goddesses the young know today play sports and movie characters, or at the very least drive BMWs and have lots of sex without consequences. They simply cannot conceive that a life with no sex and hardly any money could be for anybody but a loser.
Nonetheless, I'll venture a challenge in the form of a question. Everybody has been outraged by the clerical sex-abuse scandal. But which scenario is more likely to produce clerical pederasts and their enablers: one in which only losers are thought fit for the priesthood, or one in which real men are admired for following that vocation?