How do I fight multiple enemies surrounding me?

Solution 1:

If you're struggling with groups of enemies then there are a number of options:

Don't be afraid to ignore the combat completely. There are very few encounters that are actually necessary, most can be avoided by sneaking around them or taking an alternative path. Worst case scenario just run straight through them, monsters only tend to follow for a short time, particularly if you can break line of sight.
Pick them off one by one if possible. This can be tricky as many groups will alert other members, so you have to kill them quickly. Bombs and arrows can both do a lot of damage with out actually making enemies aware of your presence. I have killed many enemies by raining bombs down on them from a height (be aware though that even non bow armed enemies have ranged attacks and will throw rocks at you if they do spot you)
Edit: As mentioned by Batophobia in the comments you should also make sure to use the environment to good effect. Puddles of water can be exploited with Lightning Arrows, grass can be set fire to, boulders can be pushed on to enemies and metal objects can be swung around.
SGR's tip is a good one for group combat. Get a good two handed weapon and start charging an attack as the enemies run towards you, if you time it right you should be swinging your weapon around wildly by the time they reach you and you can decimate a group pretty quickly.
Alternatively get a good spear and back away while using the spears reach to take out the closest enemies until the group has been thinned a little.
Always watch out for archers. Two or more archers plus some melee enemies can cause you a lot of trouble. If you can sneak in and kill any archers first (or make a beeline for them and take them out first) this can really improve your chances.
Do some more Shrines and get some more heart containers. Try and find some better weapons or improve your armour. I struggled a bit with combat at first but with better armour and weapons and a little practice I rarely get in trouble at all.
Make use of cooking to create food and elixirs. You can always eat from the menu, so if you are reduced to low health you can eat to heal yourself (as long as you have prepared items, some raw foods heal but not as much as cooked foods). You can also cook food to provide many different bonuses, like extra attack or defence. As Batophobia mentioned in the comments a bonus hearts meal is particularly useful because it also fully heals you.

Solution 2:

One last ditch method, provided you can buy enough time to pull it off, is to use the special attack of a Two-handed weapon (not a spear).

Simply hold down the attack button while having a two handed weapon equipped and Link will start spinning. Two handed weapons have a greater chance of knocking an enemy back or otherwise stunning them, and the special attack causes you to attack all 360 degrees around you. This should hopefully knock down a couple of smaller enemies and stagger bigger ones, allowing you to get away.

Solution 3:

If you encounter a bigger group of bad guys it is usually a good idea to keep them all the time in front of you. You can do so by focussing one and jump backwards until everyone is in front of you. Then you could use a weapon with higher range (like a spear or a two-handed sword) an attack them.

But keep in mind: Are you already prepared for those enemies? Do you have enough hearts? Is your armour high and your weapon strong enough?

It is also a good idea to use a shield. It is also easier if you already unlocked Daruk's Protection. Maybe you should practice the counter-attack?

You could also use some of your bombs. Try to get some distance to the group and throw one. This separates them and knocks them down.

Solution 4:

Having never played the game (sadface) I can't give any specific advice. However, I can give some more general advice on how to deal with a large group of enemies:

"Pulling": Depending on the AI of the enemies, this is a possibility. It also depends on the range of your bow. Essentially, stand outside the range of your enemies aggro range, and shoot at one enemy. This will either do 1 of 3 things:
- Optimally, you want them to be attracted (or aggro'd) by the damage, and come at you on their own, so you can deal with them 1-on-1.
- They won't react at all. This allows you to simply pelt them with arrows, with no harm to yourself.
- It will attract them all. This is, clearly, what you don't want.
"Thin the Herd": If pulling doesn't work, you can instead use other tactics to reduce the overall numbers in the group. Bombs work well for this purpose, if you have them. Any kind of AoE attack, really.
"Hit and Run": If the first two options are off the table, your only real options are to hit them once, then run away. Once they're behind you again, go for another swing, then run away. Rinse and repeat until they're all dead. This is similar to...
"Kiting": This method basically means running away, until you have a single-file of enemies chasing you, giving you a 1-on-1 fight. This does require a lot of moving around, so be prepared.

Once you've found a way to deal with the majority of the group, you can then re-engage them in a more aggressive manner, dealing with them head on.

Solution 5:

Obviously having more health, doing more damage and taking less damage are going to make fights easier. However, that's a long term investment in finding and completing shrines, gathering materials to upgrade armour, etc.

Some approaches I've taken to large groups while playing the game:

Take out the weakest enemies first. The aim is to reduce the size of the group as quickly as possible, so kill the enemies that only need a few hits first, then you can focus on the stronger enemies without worrying about being surrounded. If you're not using the Champion's Tunic to see enemy health, the enemies are colour-coded so you can tell which are the weakest ones (off the top of my head I believe it's brown, blue, black and silver, in ascending order of strength).¹
Start the fight from as far away as possible. This generally gives you the most time to take out enemies with your bow before they reach you. You can also throw down bombs ahead of you and detonate those when the group starts to get close to give you even more time.
Use terrain as much as possible. If you're in a location they can't reach then you only have to worry about ranged attacks, which are usually more telegraphed and easier to dodge. This can require a large supply of arrows, though.
Make your hits count. If you're starting from range, aim for the head; hitting enemies in the head with an arrow will do double damage as well as stunning them.
Freeze enemies in place. The upgraded Stasis+ power will allow you to stop time on an enemy, in addition to objects. However, it generally has a very short duration so may not help too much. Freezing enemies with ice arrows has a much longer duration, so you can freeze a group and then pick them off a few at a time (this is one of the tips from the loading screen).
Use stealth. You can obviously avoid the fight entirely in a lot of situations, but if you do want to engage, taking a stealthy approach to begin with can make your life easier. At night, enemies will sleep; you can sneak up on them and benefit from sneak attacks which do vastly increased damage.
Take their weapons away. Enemies will often also leave their weapons and shields lying around, rather than holding them, so you can sneak up and steal them. Knocking an enemy back with a large two-handed weapon or shooting them with a lightning arrow will often cause them to drop whatever they're holding - if you have inventory slots free, grab their weapon(s) so they can't use them against you.

¹ There seems to be an element of enemy scaling based on how far through the game you are, so if you're just starting out you may not have encountered many of the higher level enemies yet.