I'm trying to understand how as a GM to handle encounters with creatures such as wolves, bears, giant rats, etc.
Are animals always hostile to the PCs or is there always an element of animal handling involved?
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Few creatures that the PCs encounter are single-minded killing machines, even for “monsters”. Animals are even less suicidally-bloodthirsty murder-machines. If you don't already know the attitude of a monster, especially of an animal, when the PCs encounter it (i.e., you haven't already decided that this wolf attacks two-legs on-sight because it's been driven insane by the local orcs tormenting it for fun, or whatever), you need to decide what your creature thinks of these creatures it has just encountered.
Pages 244–5 of the DMG to the rescue! The beginning of many fights are actually (sometimes very brief) social interactions: the two sides react to each other first, sizing each other up to figure out whether they're a threat or an opportunity. These guidelines give DMs a quick idea of how to handle these situations.
First decide what the attitude of your creature is. Animals will often be Indifferent, though sometimes Hostile if the PCs' presence is inherently threatening (like, they just walked into a wolf's home).
When you're not sure if an animal is Hostile, default to Indifferent (qv. animals not usually being bloodthirsty killing machines).
Portray this attitude to the players as you describe them meeting the creature. An Indifferent animal will observe them carefully, perhaps warily, but will not display threatening behaviour. An Indifferent creature doesn't want to start a fight for no reason, after all — it's indifferent. Even a Hostile creature is — contrary to popular media and video game depictions — not going to leap at the nearest PCs' throat on-sight. An actual hostile animal rather displays threat behaviours to warn or scare off intruders or perceived threats: growling, making themselves look bigger, and generally saying “go away” or “I can hurt you if I want to” with animal body language.
The exception is an animal that is Hostile because it's desperate (perhaps desperately hungry): these have already decided to attack, and it's just a matter of figuring out when and how to strike. Figuring out motivation details like can help to portray an animal in an interesting way. Desperate animals are generally the exception though, so it's better to default to a more normal, non-desperate motivation for the animal encounter, such as “whoops, we accidentally ran into each other”.
Whatever the animal's attitude, portray it to the players so they have information to make decisions with.
If the players do anything that's not attacking — shouting or throwing things to scare it away, talking in low reassuring voices while walking away or towards the animal, offering food, etc. — then continue handling this as a social interaction. Use the Charisma check method on DMG page 245 as a default way to determine how the animal reacts to the PCs' actions, or a more specific skill if the PCs are trying something more specific than just communication (like Animal Handling to calm the animal, or Insight to learn something about its behaviour, etc.).
If the PCs do things to anger the animal enough to inspire it to violence (maybe it's Hostile and they try to make calming noises while trying to walk past it, but flub the Charisma check and get the “The creature opposes the adventurers' actions and might take risks to do so” result), or if the PCs just straight-up attack, then the social interaction has become combat! Do the combat thing.
Even if combat results, the animal's original attitude might still be useful to you though. You can use it to inform how much it will fight or whether it will try to simply defend itself long enough to flee, for example. With the original attitude and motives in mind, you'll find it occasionally inspires more interesting fight scenarios than does the motive to just kill or be killed.
If you are referring to Beasts, they are often Unaligned. From page 7 of the MM:
Many creatures of low intelligence have no comprehension of law or chaos, good or evil. They don't make moral or ethical choices, but rather act on instinct. These creatures are unaligned, which means they don't have an alignment.
In this case, I think that these creatures behave as in the real world: they may be hostile in certain conditions, e.g. if they feel threatened or if they are hunting. As the description says, they follow their instinct. The DM may consider a animal handling check is he thinks that there is the chance to calm the creature.