Find - Yuzu is difficult to find outside of Japan and Korea for a couple of reasons.  First, the supply and demand are both somewhat limited.  Yuzu is primarily grown in Southern Japan (especially Kochi prefecture)

Choose - Look for bright, fragrant fruits.  Most commercial yuzu is fairly unblemished, but untended or semi-wild trees are often affected by a fungus that causes black spots on the peel of the fruit (citrus melanose). This generally doesn't affect the flesh of the fruit, but affected fruits are generally not favoured for purposes where the peel is to be used.

Yuzu has a somewhat loose, easily peeled skin, which may make them feel somewhat soft. This is normal. The fruit beneath the skin should still feel fairly firm.

Ripe fruit should be quite juicy, but it’s not uncommon for voids to appear in the segments around the numerous seeds, and in the space between the peel and the fruit segments.

Store - Yuzu can be stored at room temperature (e.g. in a fruit bowl) for at least a week assuming that they are not already over-ripe, but (as with any citrus) keep watch for any powdery mould growth on the skins. If you want to keep them a little longer (or stop them from ripening further), they can be kept in the refrigerator for at least two weeks (and often longer).

Yuzu fruit may or may not be waxed.  Unwaxed fruit is a bit more prone to spoilage and moisture loss, so bear this in mind.

Yuzu freezes very well if kept whole, and the juice can be frozen as well.

There are a number of yuzu cultivars distinguished by their growing qualities, and by (relatively) subtle differences in fruit quality.  In general, these varieties are not likely to be distinguished at a commercial scale, but it if you happen to be in Kochi Japan and you have the luxury of asking around here are some of the types you can look for:

• Kumon, Nagano, and Kiyotou are considered to be especially valued in the yuzu growing region of Kochi, Japan.
• Tadanishiki is a seedless yuzu cultivar.
• Komatsu Sadao is a variety that is notable for containing particularly high quantities of the fragrant compounds responsible for giving yuzu it's distinctive fragrance.
• Other varieties include Jimoto, Komatsu Koichi, and Yasu, though there is little information available about these.

Most commercial yuzu is grown on trees that have been grafted to a root stock (generally on trifoliate orange), but seed-grown (misho) yuzu can fetch a premium as a gourmet product.  Misho-yuzu is often grown in mountainous areas, and harvesting the fruits from the rather tall trees can be very laborious.

Shishi Yuzu (below) is an unusually large, gnarled yuzu fruit, particularly popular for use in yuzu baths.  It's not commonly used for culinary purposes.

Shishi yuzu fruit from Kuromon Market in Osaka, Japan.

Yukou is a rare Japanese citrus that is sometimes regarded as a sweet yuzu, but it is most likely not closely related.

Yuzu is highly distinctive, and therefore difficult to accurately substitute for in a recipe.  Given the difficulty of finding fresh yuzu, the best substitute for fresh yuzu is generally going to be bottled or frozen yuzu juice, plus or minus lemon zest (or dried yuzu peel, if you can find it).

If you can't find any yuzu products to work with, there are a few options you can explore.  Note that these substitutions do not replicate yuzu per se, but instead achieve the same sorts of effects in recipes.

Lemons and lemon juice make an acceptable alternative to yuzu.  Lemon lacks the distinctive fragrance of yuzu, but does have a wonderful aroma and flavour of its own.  Lemon can also be blended with yuzu if you're short on the latter.  If you can get less ripe (or even green) lemons, they can be nice to use, as they're a bit more sour and herbal.  Note that Meyer lemons do NOT make a great substitute for yuzu, as they're too sweet.

If you want to avoid an overly distinctive lemon juice flavour, try substituting a mixture of lemon juice, grapefruit juice, and a little bit of lime juice.  A 4:2:1 mixture is a good place to start.

Similarly bold and sour citrus fruits can make excellent alternatives to yuzu.  These include sudachi, kabosu, kalamansi, rangpur lime, and Seville orange.  Note that these are alternatives, not substitutes; they taste very different, but like yuzu, they are sour, fragrant, and slightly bitter.

The peel and zest can't really be replicated, but lemon and citron are closest overall. Other citrus peels can provide similar flavour profiles in dishes.