How to play - Riki (Agility)

Rikimaru is an agility based hero. He relies heavily on items, so unless you have a good support hero with you that has plenty of stuns/slows then it's probably not a good idea to choose Riki. Riki is best against squishy heroes such as Kunkka, Lina, and many other heroes that have low armour and low HP. Riki works so well against these characters mainly because of his Smoke ability, which causes the opponent to be slowed and also silenced. There is nothing like spotting a squishy alone and blinking in and smoking.
Now a brief explanation of Riki's skill set and applications.
Q - Smoke
Getting the timing of a smoke right is critical to being a good Riki. It can stop the most powerful Intelligence heroes from casting their 1 hit ulti's (such as Lina's Laguna Blade), which can be devastating to Riki's HP. Its always a good idea to smoke your target, auto attack a little bit (from behind if you can), and if the target isn't dead Blink after them.

W - Blink Strike
Blinking is Riki's main chase function, or even an escape route if things go bad. It allows Riki to blink next to the target and perform an attack which deals bonus damage. Generally i save the blink for chasing a target, but some people like to initiate on a blink, which in my opinion doesn't really work, because even when the cooldown is maxed at 5 seconds i have been caught with my blink down and either A) Been stunned and nuked, B) Been chasing someone near a tower at 10 hp and not being able to blink them. The blink is very instinct based, if you think you can keep up with the hero (E.g Tidehunter) then you can probably pop it however,  if its a hero like Night Stalker, then it's probably a good idea to just smoke the bugger, then pop your blink to make up the speed difference.

E - Backstab (Passive)
Riki's backstab ability is the gem that helps you get those last hits of the creeps you need to farm the hell out of. It gives extra damage based on a percentage of your Agility points when you are behind a target. Early game it's not great, but mid-late game it can be devestating. The amount of times i've been in a team fight and someone hasn't spotted me behind them is ridiculous. The bonus damage does help A LOT in the late game, but it is a skill to be able to position yourself for the skill to trigger.

R - Invisibility
Invisibility is an absolute god-send if the opposing team does not choose either A) Slaardar or B) Bounty Hunter. It allows you to scout out the map, and catch people on their own. This is especially good for catching out a jungling Ursa early-game. The only downfall with Riki's invisibility is that at level 1 it takes 3 seconds to go back in to invisibility when you break it with an attack. Although with practice if you get caught out by the break you can blink somewhere and evade the gank.

Items
When I start as Riki I usually get 2 Slippers of Agility and A shield, then just buy the shield recipe from the side shop. Although less experienced players may choose to get 2 slippers, a shield and tangos/salves.
Now as far as mid-game items it is usually just preference and also depends whether your team has stuns/slows. Some people say that Diffusal Blade is great for Riki mid game, but I personally have found it better to buy Vlads and a Sange/Yasha. This is because if your team has a nice set of slows and stuns then there's just no point to buying the DB, the extra attack speed and damage from the S/Y just ends up being so much better.
Late-game (Or when your just fed like an Obese whale) then i would probably go for a Butterfly. The evasion is just a troll, and the attack speed increase is dangerous to any opposing squishy.