Lane Properly:
Talon is very good at farming. Level up his rake(W) as fast as possible to 5. This can essentially one shot a minion wave. Many people at lower levels do not understand the importances of balancing harassing with farming. Farm up well early game, dominate late game.
If Talon is laning with a partner, choose a partner with good crowd control. Talon can easily harass with his rake while still farming. Just use it while the enemy is standing by the minions you are trying to kill. When an enemy is low enough, get the partner to stun or snare and you can cutthroat in and use to burst to bring down the enemy. Note that cutthroat will not only increase your damage but silence the enemy so that they cant ghost/flash or use one of their spells to escape before you kill them.
If talon is laning top solo, once again focus on leveling up rake and farming with it. But with talon being alone he can harass more aggressively by using cutthroat to silence the target, use your skills and run away before the silence ends. This usually results in you dealing a lot of damage to the enemy than they can retaliate with.
When to engage:
I assume you mean in a teamfight. There are two ways to play talon in teamfights. The first way is to play like a normal assassin and stay behind your team hidden. Only when the team's initiator(tank/offtank) go in and the fight has started so you go in and focus their ap carry. I say this because talon has a silence which will prevent their ap carry from doing any damage.
Another way to play him that most people are usually reluctant to do is be the initiator. This will work really well if the opposing team does not have too many stuns and/or do not have oracles. You basically cutthroat into their ap carry and immediately ult to stealth. This will cause them to immediately switch to another target(preferably your tank/bruiser who has come in by now). A benefit of this is, you get to damage everyone with the beginning of your ult AND the end of your ult.
Build:
Talon is as I've said before a burst assassin. He bursts and then runs off. So if anyone ever tells you to built attack speed on him. DON'T. Build pure AD and armor pen on him. You shouldn't have to stay and autoattack because any tanky AD DPS can kill you in a toe to toe fight
I would start with dorians blade first. At first recall, hopefully enough gold to buy a pair of boots and the brutalizer. Next built the boot into Ionian Boots for the CDR (Once again berserkers's attack speed is less desirable compared to CDR where you can burst more often), and start of the blood thirster. Then i would finish the brutalizer into Youmuu's GhostBlase and bloodthirster. Afterwards i would built last whisper (that 40% armor pen is OP!) Infinity Edge and Another Blood Thirster to finish.
Runes:
When runing a champions there are two things to keep in mind. Do you normally have trouble early game and would like a early game advantage or do you do well early game and want to have runes that scale really well into late game.
If you do not do very well early game and need all the advantage you need, then build flat AD Marks. But if you do well and want runes to scale better late game, built Armor Penetration Marks.
For Seals, I would take flat mana regen(replenishment) because talon is pretty mana starved early game if he wants to farm well and still harass.
For glyphs i would take flat cool down reduction.
And for Quintessances, i would take Armour Pen.
Masteries:
With the new change to the mastery trees, assassins like Talon can rejoice! I won't tell you exactly which to put points into but focus on the offensive tree for assassin champions like talon who focuses on burst.
Summoner Spells:
The two I would recommend is: Ignite and Flash. Flash is of course one of the most powerful summoner spells there is. This can be used both offensively and defensively. If the enemy is just out of reach of your cutthroat and you can't jump to them for the finishing blow, flash will close the gap between you. Or defensively you can use it to create a greater gap between you and your enemy OR flash over a wall. You do not understand how many times that has saved my life.
Ignite's DOT and his Q's DOT does a surprising lot of combined damage. In addition ignite will reduce the amount of healing the opponent have/gets. So if you are laning against someone with heal or a lot of life steal, ignite will make you laugh gleefully as they die because they can't heal themselves from your burst.
AP champions scale best off of levels so by putting them in a solo lane they earn the most experience. Mid lane is the shortest lane so it is easy to escape compared to top, which is generally the realm of bruisers who can survive ganks and have gap-closers.
Some APs are excellent roamers and having them in mid allows them to influence the other lanes. Ahri, Sion, and Leblanc are all vicious roamers that can quickly get kills in other lanes due to their burst/CC.
AD champions scale best off of gold so they get a support to help them farm safely. A lot of the times the support gives sustain to make this farming easier.
Having two people in bottom lane also allows for control over dragon, which is a very important objective early on. Baron doesn't normally become an issue until well after laning phase is over.
However, sometimes you will see pro teams throwing a solo champion bottom if the champion can handle fighting two people at once and still farm. They do this so their AD carry can abuse the enemy top lane and free farm.
Best Answer
A Talon vs an AP champion looks pretty good on paper. Let's break it down.
Abilities
W Rake: Deals AOE physical damage to a wide area in front of him and slows enemies. The popular AP mids have good creep clearing abilities that could push a traditional ranged AD back to the tower, which then allows the AP champ to gank side lanes. Rake checks this. Although Talon is melee, Rake allows him to safely clear the creep wave when needed. The slow is also nice for ganking and chasing.
E Cutthroat: Instantly appears behind a unit and silences it for 1 second and amplifies subsequent damage dealt to it. This is the key for applying pressures on AP champs. A silenced AP champ feels like a sitting duck and an inexperienced player will try to run, giving Talon a free auto-attack. Cutthroat also resets the auto-attack timer, so you can actually hit twice. Although the silence can be blocked by spell shields, the ability is instantaneous, which makes it very difficult to react against it.
R Shadow Assault: Becomes invisible for 2.5 seconds + 40% movement speed buff (Ghost is only 35% with the mastery); his blades deal physical damage in an area around him. Great ult for a mid laner to have. It makes him extremely difficult to gank, gives him a great chasing mechanic and is a great ganking ability. Plus that 2.07 bonus AD ratio if you Cutthroat them first - ouch.
Stats
Magic Resist: Talon has scaling magic resist. Nice. Most AP mids don't have this extra defense (usually melee champions have scaling MR).
Health Regen: Talon has ~150% the HP regen of AP mids. It'll take much more to harass him out of lane and an AP champ would rather be using that mana to farm.
Movement Speed: Few AP mids (I think only Katarina) have such high base movement speed. This make Talon great at dodging skill shots and ganking side lanes.
Health: He starts off with about an auto-attack's more health than most AP mids. It's a small but comforting advantage in the early levels.
Pick
Talon is rarely picked in ranked games. There's either a more nuanced explanation for his weakness in other parts of the game, or he's just underappreciated. On paper, he looks very strong with a Maw of Malmortius.