Without using "magic" knights do not kill anyone either.
First off, we are going to split this into three level ranges.
Low level (below 110)
You will usually need the help of other players or monsters here. Unless you have very high skills your damage is rather limited. With the addition of the crit imbue it has become possible to (solo) kill other players at this level but luck is involved. At level 60 you get Blood Rage (Utito Tempo) to increase your damage by a lot.
Try to stay ahead of your target, block critical passages. If you are trying to kill someone in a spawn keep an eye on the monsters and try to use them to your advantage.
Combine your normal weapon hits with spells (magic? haha) and potentially even monster hits.. Keep in mind that Blood Rage increases the damage of both your hits and your spells.
Mid Level (above 110)
Here you get your most valuable spell for pvp. Annihilation or exori gran ico.
This spell combined with a normal hit can combo for big amounts of damage. (Plus obviously Blood Rage to increase your skills)
Catching a mage off guard with this combo can often lead to a quick trip to temple.
It has one downside though. After using it you will skip one attack turn (Just like mages after using their ultimate explosion), If your combo does not finish them off they have a long time to react..
High Level (200+)
You unlock your vocations summon. Skullfrost is a very powerful tool to increase your damage. You basically do the same thing as you do on the previous levels with the addition of your summon. Once you see it blasting the target you can try and throw in your Annihilation and hope that the target dies.
As mentioned earlier your damage is related to your skills. So any equipment that boosts your weapon skill helps.
The one easiest obtainable would be a skill ring which provides +4 to the respective skill.
Additionally you can imbue your weapon and helmet with the desired skill for extra bonus skills as well.
Some items have bonus skills attached to them naturally. The silver token armors provide an extra +4 for example. At this level you can also use the amulet of red plasma.
As for weapon choice, if you are pumping someone and try to take them down over time / with monsters a weapon imbued with critical strike is your best bet. If you only want to combo someone from 100 to 0 the most consistent way is to use a glooth weapon though. These weapons, much like the old ice rapier, provide a very high attack at the cost of breaking. They have two charges and let you combo someone with a normal hit + a spell before breaking.