Now, before we get into this, there are two things you should know about: IVs and EVs. IV stands for Individual Value, and is a value from 0-31 that determines the stats of a Pokémon. Each Pokémon's IVs are determined when you catch or breed it, and can't be changed. Pokémon have one IV for each stat, so one Attack IV, one Defense IV, and so on. IVs are what make each Pokémon unique, and why two Pokémon of the same nature have completely different stats. (IVs are like a Pokémon's genes; everybody's different.) IVs also determine what type attack the move Hidden Power will be.
EV stands for Effort Value. Each Pokémon starts with 0 EVs, and gets more as they battle other Pokémon. Each Pokémon is worth a certain number of EVs; for example, Scyther is worth 1 Attack. A Pokémon starting with 0 EVs that defeats a Scyther in battle by itself will end the battle with 1 Attack EV. 4 EVs in a stat equate to one point of stat growth. Pokémon can have 510 EVs overall, with 252 per stat.
Generation VI greatly simplifed this whole process by introducing Super Training, allowing players to train for EVs more efficiently, and without having to know which Pokémon are worth what EVs, and so on and so forth. (Let me tell you, it was a pain in the ass before then.)
So, what's the best way to train a Scyther? Full disclosure: I'm not into competitive battling, I mostly just battle against the NPCs and whatever the current gen's version of the Battle Tower is. If you're looking for competitive strategies, spend some time at Smogon. Scyther's a tricky Pokémon to use given its 4x weakness to Rock, but it can still be a lot of fun to have.
natures & evs
Given Scyther's two best stats — Attack and Speed — you should have a nature that boosts either one of those, and decreases Special Attack, since Scyther will never use it. That leaves you with either Adamant or Jolly. Jolly is probably a better bet, as it ensures that Scyther is the fastest Pokémon on the field.
Again, given Scyther's strengths, your best EV spread is generally going to be something along the lines of 252 Speed, 252 Attack, and 4 Defense or HP. You can swap Speed or Attack out for HP or Defense as needed, but Scyther's primary role in battle is to hit fast and hard and not spend much time on the battlefield; it's no tank. Get it in, let it do its thing, and take it back out.
Scyther should always run with Technician; its other abilities are of no use. The Eviolite (a held item that boosts the Defense and Special Defense of Pokémon that can evolve) is the best item to give it unless you're using a different strategy that requires a different held item.
A straightforward set that skyrockets Scyther's attack and lets it use its STAB attacks, plus a Fighting-type move to deal with those Rock-types it's afraid of. Scyther can't take a lot of hits, but its attack is high enough to slice through a lot of Pokémon. A good all-around set.
Similar to the last, with the difference that Scyther is used as a scout to see what the opponent is sending out. If Scyther is holding a Choice Band or Choice Scarf, its Attack or Speed will be 1.5x more, respectively, making it that much more useful. This keeps Scyther safe while still letting it inflict damage.
This isn't a set for use against other trainers, but rather for catching Pokémon. Scyther is one of the best Pokémon to learn the move False Swipe (which damages a Pokémon up until it hits 1 HP) given its high Attack and Speed stats. If you've got a legendary Pokémon to catch, take Scyther along and have it use False Swipe. The rest of this set is geared to cover as many types as possible, so that Scyther's still viable in battle. I used a modified version of this set for my X playthrough.