How do monasteries support themselves? Barely.
At least in Canada, and from everything I've seen of the situation in the US, it's a matter of "do what you can". Gardens and such are a bit harder in Canada, depending on the latitude, as the growing seasons can be a fair bit shorter than, say, Arizona. But, often, monastics try to grow as much as they can, but it's unlikely, at least around here, that they can be completely self sufficient through a garden.
Often monasteries sell candles, and other things like soap. If they can rig up the equipment, and develop people who know what they're doing with it, this is a good money maker, with a fairly good profit margin. Plus, it's rather condusive to monastic life in that one can make candles whenever one has time in between services, etc. Same idea with baked goods, or whatever. There are a few that have made a go of running a printing press. They use the talents they have in any sort of "cottage industry" that is viable.
That and of course, they don't turn down donations, but it's actually rare, and somewhat dangerous from the point of view of the monastics, to entirely depend on donations. They work very hard to avoid that kind of dependance.
As an absolute last resort, outside secular employment has occasionally been used. It's not the best situation, but hey, at least you don't starve to death. That's the situation I find myself in at the moment, and I'm not alone, although I'm also not keeping it a secret that I'm taking steps to move to a more established monastery in the US. Lots of hoops to jump through for US Immigration...
WRT having some sort of skill to make you more "attractive" to a monastery, don't worry about it. It's often only after a person comes to a monastery intending to stay (as opposed to a pilgrim) that they discover they have talents and abilities that they didn't think they had. Accountants can discover they have a real knack for making candles - construction workers can discover a talent for administration. Academics with enough degrees to choke a horse have found real satisfaction in making sure the sidewalks are swept and the dishes done after meals. Chaps that barely graduated high school can end up translating obscure texts. More often than not monastics end up doing things that they never dreamed they would be doing when they were in the world.
When they talk about monastic tonsure as a second baptism, and someone starting out a "new life" in monasticism, they mean it
. It's amazing to discover how often new talents, abilities and skills develop within the monastic life. They really do become a new person.