Combat in Fallout 4 isn't as simple as picking up a weapon and battering the first person you find. At least not all the time, it isn't. There are a few key elements that play a part in picking a successful fight in the Commonwealth, so it's best you make sure you understand the basics of them all.
Using VATS in Fallout 4
The Vault Assisted Targeting System is extremely useful and versatile when you're fighting in Fallout 4. When you activate your VATS system everything goes into super slowmo and you can target and shoot the individual body parts of your enemies. The percentage chance you have to hit that body part is displayed over them, and will change based on how close the enemy is and whether they're behind cover (it's also affected by the weapon accuracy and your own stats). You can flick between different limbs and different enemies as you like, but the number of targeted attacks you can make while you're in VATS is limited by your Action Points (AP) and the type of weapon you're using.
There are a bunch of Perks to explore that increase your VATS accuracy and add other bonuses. You can also use VATS to target grenades and molotovs once you've thrown them for an immediate detonation, which is pretty cool.
How Action Points work in Fallout 4
Your Action Points (AP) determine how long you can sprint for, and are also the pool for your shots in VATS. Generally speaking the better rate of fire or speed a weapon has the less AP it burns up, though this can be changed by modifications to your weapons. You can also get the Action Boy/Girl perk to increase your AP regeneration, and there are different chems or foods you can use to buff your maximum AP for a short while if you're in a particularly heavy fight.
Limb damage and crippling in Fallout 4
When you target any part of an enemy the bar underneath indicates the status of that particular part, separate to the target's health as a whole. If you repeatedly shoot the same limb you can wear down its status bar until it's empty, at which point that limb will be crippled. This does different things depending on what it is you've targeted. A crippled leg, for example, will hinder their movement. You can use this pretty tactically: on radscorpions you can shoot off their stinger and you can destroy the weaponised arms on robots to make them way less of a problem. It's even possibly to cripple an enemy's head before you actually kill them, although as you start dealing higher amounts of damage you're more likely to just murder them outright.
Keep in mind that you can be crippled yourself, potentially slowing you down or making it harder for you to aim. In order to cure yourself of being crippled you have to use a stimpak, even if your health isn't actually that low.
How damage resistance works in Fallout 4
Everyone in Fallout 4 has a resistance score for three different types of damage,including yourself: ballistic, energy, and radiation. Your weapons will deal one of these types of damage (or sometimes a combination, depending on what you're going with), but you also have to take into account the resistances of whatever you're attacking - the Awareness perk under Perception will display exactly what resistances a targeted enemy has. The damage will be reduced by the amount of resistance as a percentage, so an enemy with energy resistence of 45 will receive energy damage reduced by 45%.
This is important to remember when you do things like sort your weapons by their damage score: a weapon might technically have the highest damage, but not when applied to certain enemies. Most mutated animals, for example, and that includes supermutants and ghouls, will have incredibly high resistance to radiation damage, up to taking none of it whatsoever. Attacking them with an irradiated weapon like a gamma gun will do basically nothing, whereas ballistic and energy weapons will have a more substantial effect.
Critical Hits in Fallout 4
In previous Fallout games any successful hit had a chance to become a Critical Hit, but in Fallout 4 you activate them manually in VATS yourself. You have a metre which gradually fills up with each successful attack you make in VATS, based partially on your total Luck stat, and when it's full you can activate a Critical Hit, which will be an automatically successful attack and deal multiplied damage. You can only have one Critical Hit banked at a time, unless you have the Critical Banker Perk. Other Luck Perks will increase your critical damage or give chances to refill your critical meter.