First off, it's important to decide what type of yukkuri you want and how you will get it. Most would desire a yukkuri that is well-behaved and complacent. It is recommended that beginning anons should start off with a yukkuri exhibiting those mannerisms, most likely a nicehead Reimu or a Byakuren, or a Daiyousei.
Next, you need to decide where you are going to purchase your yukkuri. You should usually buy a koyukkuri, as it will be easier to train in behavior and the like due to its young age. Any yukkuri can easily be found at a pet shop, however if yukkuri are particularly reckless it is recommended you get a Satori to calm it down. You can also find a yukkuri in the wild, in its natural habitat if you're the adventurous type.
At pet shops you can pick up a newborn yukkuri, but it is possible to care for a koyukkuri if the parent is already pregnant. There is a stalk growing from its head with the baby attached, but if it falls off prematurely there is no need to worry. Feeding it with warmed sugar water will help it grow properly. Remember that when a baby yukkuri falls from its stalk, it is extremely fragile - similar to an actual human baby - and thus can hurt itself. It's best to place a pillow or some soft grass underneath to cushion its fall.
Now that you have your yukkuri, congratulations! While every yukkuri is different and therefore requires different accomodations - a Kaguya yukkuri will most likely be heavily spoiled and require electronics, a Flandre yukkuri will require lots of food and attention - here are some basic care methods to help you.
Feeding your yukkuri Edit
Taiyaki and other foods with bean paste are a favorite among pets, possibly because of the similarity to its filling inside. Other snacks like tea candles and mochi are well-liked, particularly by the Reimu yukkuri. It is important to remember that Western yukkuri such as Marisa may not enjoy these snacks, and might require something like a cupcake or an eclair to satisfy it. In fact, as long as the snack or sweet isn't sour your yukkuri will probably be happy to eat it.
If it a wild yukkuri, it may prefer something like caterpillars, honey, or berries. Some species, like the Remiryas or Flandres, will eat other yukkuri. Don't be alarmed. It's a part of their predatory nature, and can be easily discouraged.
Recall that koyukkuri require smaller dosages of food because of their size, in particular crumbs or soft foods to assist. Make sure that your yukkuri does not gorge itself on food, as this can lead to obesity.
Keeping a koyukkuri safe Edit
Keep all sharp objects out of reach from them until they are older. They do have a quick growth rate, but like any other baby or pet you must keep them unharmed until they have left their juvenile stage.
Cleaning poo poo Edit
If a yukkuri poo poos, clean up the mess with a tissue and throw it away, making sure that the yukkuri does not eat it. If the poo poo has hardened, warm up a wet cotton cloth on a stove for 10 seconds and use it to wipe the affected area. After that, carefully remove the poo poo with a Q-tip or cotton bud.
If the yukkuri has diyurrea, you should take it to your local yukkuri doctor to see how you can help it.
Showing affection for your yukkuri Edit
They will often chirrup, "Take it easy!" towards you. It is recommended that you let them "take it easy" and take it easy yourself as well.
Rub it as a sign of affection with the tip of your finger, as this will strengthen the bond between you and koyukkuri as "parent" and "child". Not only is this a way of comforting your koyukkuri and keeping them happy, but it also will tend to become hostile towards you if you refrain from doing so.
With all said and done, good luck and have fun caring for your yukkuri.