Anthro art create furies show humans in animals like fan-fiction.
The furry fandom is a subculture interested in anthropomorphic animal characters with human personalities and characteristics. Examples of anthropomorphic attributes include exhibiting human intelligence and facial expressions, speaking, walking on two legs, and wearing clothes.
You might have heard of a phenomenon called the uncanny valley. Generally, the more realistic the face, the more we like it, until it gets almost real, but not quite. This little lack of realism is much more unsettling than stylization, because we see clearly all the face isn't. You can use this information to keep your anthros "real enough"—stylized in a convincing way, but far enough from the uncanny valley to avoid comparing it to the real thing.
Finally, when your character has a full, roughly sketched body, you can start adding details to it. Does it have hands or paws? What do its feet look like? What does it wear, what clothes, what jewelry? This is the most fun part about designing a character, but there still should be nothing random about it. Even the details should be functional!
The feet, for example, are used for walking, not for looking cute. The paw pads are not random—they're cushions for the bones in the foot. If your character is bipedal, do paws instead of hands make sense, if it doesn't really use these "feet" for walking? You need to think about all these things if you want to finish the design in a convincing way.
It's not only about anatomy. The jewelry, clothing, and armor must fit the body and allow for natural movement. Don't just draw a bracelet on every empty area of the skin; try to become this character for a while and see what you would wear and how if you were them. Maybe long, dangling earrings are not a good idea for a hunting cat-man? Is wearing a skirt wise if you're moving by hopping? If you keep thinking this way, you'll avoid mistakes that break the illusion you're trying to create.
Simplification can let you drag the attention to what really matters in your design. Make the feet flat, exaggerate the muscles, make the eyes huge and expressive as in manga characters—and you'll make it clear that it's not realistic because it's not supposed to be, not because you didn't know how to do it.
Simplification removes the unnecessary elements and exaggerates the important ones, but you need to do it consistently to create a convincing image. For example, a nose made from a simple shape without the nose holes will look good only if the rest of the face doesn't have too many details. Otherwise, the lack will be visible and unsettling for the viewer.
Flexible lips are another thing. If you take a close look at human lips, they're actually a rim of skin curled out. In us and other mammals, this part of the skin has its own muscles, so that we can suckle when we're babies. Because of this, we can move them, though humans have taken it to an extreme—the motion of the lips sends emotional messages as well. Females tend to have fuller lips, which is an easy way to accentuate the sex of your character.
Lips are also important for talking—notice how you pronounce 'm', 'p', 'b', 'f', 'w', 'v' (talking birds can have problems with those). If your character is a bird, you may have to use a compromise—you either keep it realistic and never use any expression around the "lips", or treat the opening of the beak as normal, human lips.
Humans have a lot of tiny muscles in their faces used specifically for creating various facial expressions. We can also recognize the smallest change in them to interpret the mood of the other person. Animals, though they have a repertoire of facial expressions suitable for their species, are not nearly as expressive as us, and the whole body matters more in their communication than in ours.
Because of this, simply attaching an animal head to your anthro's body will make it quite hard to treat the creature as a person. We need moving eyebrows, flexible lips, visible whites of the eyes, to convey the messages written in the language of human facial expressions. Moving the ears or changing the shape of the pupils can be just an addition—they're enough for an animal, but not for an intelligent, talking person.
This means you need to simplify the face to make room for more human-like features. The eyebrows are a must, and they have to be mobile—we can read a lot from them. Many animals seem to carry a single facial expression all the time because of fixed facial features that we recognize as eyebrows (for example, many birds of prey look angry or proud, regardless of what they feel). They don't need to have the shape of human eyebrows, but they should be capable of affecting the shape of the eye.