Garage Kit building is a bit of a niche hobby, even in Japan, so it's understandable most people in the US are unaware of them, outside of the US market which is generally aimed at movie monsters and comic book heroes/villains. I am going to discuss the Japanese GK market.
Garage Kits (often called GKs) are, essentially, a resin model kit which comes unassembled and unpainted. Some are very simple kits, with only a few pieces, while others are extremely complex with nearly 100 pieces. They come in various scales and several characters are available as kits. In the Japanese market, they are primarily aimed at anime/video game/manga characters, VN game characters, Japanese movie monsters like Godzilla, as well as old-school heroes like Ultraman and Kikiader. Some kits are extremely rare and difficult to find, while others are relatively easy to find. Prices vary greatly, which are greatly influenced by the availability of the kit, sculptor/producer, date of release and popularity of the character(s). Many sculptors even sell GKs of their original characters, which can be quite difficult to obtain after initial release. The term Garage Kit was coined several decades ago, as kits were usually only produced by big-name companies and were fairly limited in which characters were available. Builders wanted to make kits of other characters, so they began making sculpts, mods and kit-bashes of their own. In most cases, resin is mixed and poured somewhere with a lot of ventilation, so garages were usually used, thus the term Garage Kit.
Resin is toxic in it's liquid form, not only does it have nasty fumes but the dust you may produce from sawing/drilling/sanding a kit is very hazardous. As long as you take proper care in using safety equipment, there is nothing to worry about.However, a lot of the tools used can be dangerous, especially for those with small children around, so precautions are necessary to keep things safe. Kits are often made by a sculptor working for a company (like VOLKS, for example) or simply as a freelancer. The Master Kit (being the original one made by the sculptor) can be made of many materials, such as: paper clay, wax and polyester clays, like sculpey. The Master kit is then used to make (usually) silicon molds of the individual kit pieces and then resin is poured into the mold, which hardens over time and creates a resin model kit.
Building a GK takes a lot of time and effort, especially when first starting out, but they are very rewarding to build. I personally prefer obtaining a GK over a PVC of a character because I am free to customize it as I see fit and there is more gratification from seeing it on my shelf than a prepainted figure. They require sanding, putty, painting, assembly and sometimes modifications. In general, the building process is fairly cut-and-dry but there's a lot more to it than simply painting a few resin pieces and slapping them together with glue. As long as you have fun building, then that makes it a very rewarding hobby.
Kits are almost always primarily sold by sculptors and manufacturers at events in Japan, similar to a convention, like Wonder Fest and Treasure Festa. They must first obtain the copyright pass from the company that owns the rights to the character(s) and, if it is granted, they are allowed to sell the kit(s) at an event. Generally, sculptors are only given a a small amount of time to sell the kit(s), which is usually as long as the event goes on. Most events are anywhere from one day to three days, in most cases. Sometimes, if there are leftover kits the sculptor would like to sell (or if they've produced more) they can try to get permission from the copyright holder(s) again, to sell at another event. Some companies are better than others about giving permission, like Gainax for example. This is why you will always see a huge amount of Evangelion kits, even though the original series itself is over ten years old. Some kits are also only sold at a specific event or are even limited to a specific number of casts, making them even harder to obtain. Some sculptors are allowed to sell via a manufacturer website, like VOLKS or even through their own website, as the sculptor Mustang has done in the past. Unless you are able to have a proxy attend an event to get the kit for you and/or you can buy it from a sculptor/manufacturers site, you will have to buy it second-hand. This doesn't always mean the kits are "used), per say, as a lot of people attend these events to simply buy kits and resell them for a higher price on auction sites. These people are often referred to as Scalpers, for obvious reasons. You can usually find kits om sites like Mandarake, as well as Yahoo! Japan Auctions. Using Y!J requires you use a proxy or a proxy service, as signing up requires you to live in Japan; Mandarake does not require use of a proxy and they offer auctions as well as "Buy It Now" options for kits. Mandarake also has physical stores in Japan, where you can buy the kits as well. Mostly, the kits offered on Mandarake are less Scalpers and more collectors, so you will often see older kits there, not only newly released ones.
Since kits are difficult to obtain in some cases, illegal copies are often made and sold, called Recasts. The result of recasting kits with cheaper resins (and also not using the original Master Kit to make molds from) causes a loss of detail. Recasts are very damaging to the US GK market, as the sculptors are generally not restricted by 3-day passes to sell a kit, so buying a recast of their work is directly affecting their income. While recasts do influence the Japanese Market, they are generally not looked at as detrimentally damaging as it is in the US Market, since the Japanese Market kits are not continually produced and sold, they are very limited. This certainly does not make recasts an okay thing, but they are generally not looked at as offensive in the Japanese market, though there are groups who are very aggressively anti-recast. Regardless, the market still exists because the recasting is usually done in a different country from where the original kits are produced and can avoid certain laws. There are even kits referred to as Thai Recasts (or Thais) because, at one time, recasting was mainly done in Thailand. These casts tend to be very, very bad quality and are often unworkable. The resin usually has talcum powder mixed in because, the recaster feels it will make their mixed batch of resin able to pour more kits. In reality, this essentially dilutes the resin and takes it from a semi-soft form to a rock-hard substance that's very brittle and ceramic-like. Not only is the resin quality horrible, but the molds are often not maintained well, causing severe loss of detail, warping of resin pieces and improperly aligned molds makes the pieces shifted and impossible to look correct again. These are often sold on eBay and it's best to avoid them. If you want a US kit, look up the sculptor's information and contact them, they're usually very happy to have someone buy their kit(s). In the JP market, stick with Yahoo!Japan Auctions and places like Mandarake.
With all that said, this is just a general introduction into resin. Building kits is a really fun, rewarding hobby and I recommend trying it at least once.