Combat in Minecraft is, much like the rest of the game, a relatively simple affair on the surface with a few interesting wrinkles that make it a lot more without making it terribly complicated.
There are, of course, the basics- hitting things. Hitting an animal or monster with your bare hand or an object that isn’t a tool is the weakest way to attack them. The next step up is using a tool that’s not especially combat-capable- this includes the hoe, the clippers, or smacking something in the face with your bow (which just doesn’t compare to shooting it with an arrow at all). Then you have the pick, which is inferior in combat to the axe, which is beaten out- though only just- by the sword. The bow fits into an unusual spot- it deals more damage and shoots further the farther back you draw the arrow, and while it does less damage than the sword (about as much as a pick at full draw), it has the advantage of range.
Either way, the only thing affected by which thing you’re smacking a monster with in melee is how much damage you are dealing on each strike. As long as you aren’t being swarmed or mobbed, the only thing you’re losing in most cases is time (creepers are an exception- the slower you kill them, the more likely they’ll explode instead of getting toppled). Even your reach- slightly less than two blocks- isn’t altered by what you’re using to fight with.
The really important points in combat are all movement. First of all, you are faster than almost everything you can find yourself fighting. Combined with your ability to move laterally (that’s sideways) without relying on a programmed interval or timing, and your ability to leap gaps and climb while fighting, you already have an advantage over the monsters. There’s more than that too, though.
If you jump into the air, and strike on your way down, you will see sparkles shed from where you struck. This indicates that you landed a ‘critical hit’- dealing extra damage. Aside from you yourself, the only thing in the game to take advantage of this is the spider, with its tendency to pounce at you and therefore be a lot more harmful and difficult to hit than most other monsters. You can even use this to strike hard while falling from higher ground if, for some reason, that’s a better idea than jumping.
Additionally, if you run towards something and strike it while you are running, you will score a knockback hit- and rather than sending it back a short distance, you will launch what you struck through the air, causing it to land something on the order of three blocks away from where it was when you hit. This is an especially nice tactic against creepers, but can also be used to knock things into lava or off of cliffs (especially off of cliffs, since lava will burn whatever the monster drops).
Keeping these things in mind and taking advantage of them will often mean the difference between leaving all your valuables in a pit full of monsters and rising triumphant with a bag full of even more loot to bring back home.