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The Spy is equipped with four items...
1. Revolver Gun
2. Sapper Charges (2)
3. Butterfly Knife
4. Disguise Kit
The Revolver is nice for show, but shouldn't be used much if you're playing a Spy correctly. The Sapper Charges are placed upon enemy Engineer items such as gun turrets. The Butterfly Knife can be used to get a one-shot kill if you're standing directly behind the player when you are attacking. The Disguise Kit is used to change your appearance into any of the enemy classes.
The first goal of a spy is to get into the enemy base to place Sapper Charges on the enemy gun turrets so your team can progress past the defenses. If you right-click as a Spy you will activate your 10-second cloaking device and can use this to pass through the front lines into the enemy area. You can activate a disguise while you're cloaked, so do this during the 10 seconds are you are cloaked and running through the front lines - you don't want to come uncloaked and not be disguised. Also, try to come uncloaked in a corner where you're out of the enemy sight.
Once you're in their area, try to act like the class you are disguised as. If you disguised as a Scout, then run around in circles and don't stop moving, since Scouts are very mobile. I usually disguise as a Sniper and pretend to be sniping - no one ever attacks me while I disguise as a Sniper, works great.
Once you've established yourself as one of them, and you're cloak timer has reset, start your progress towards the enemy gun turrets. It's best to approach cloaked since Engineers usually shoot at anyone that approaches their turrets. Switch to your Sapper Charges and place them as you come uncloaked. Immediately re-cloak and switch to your knife. The engineer will try and shoot you once and then move to save his turret. When the Engineer turns his focus from you to his turrets, it's time to move in and back-stab him with your knife.
Another thing to remember is to always walk backwards as you descend into their base. By walking backwards you look like a team member just retreating instead of a Spy running into the base in a disguise.
Besides taking out the gun turrets, you're also responsible for taking out enemy Medics. The Heavy-Medic combo is deadly and should be dealt with fast. Just cloak past the deadly-duo and come up behind the medic for the one-shot knife kill. If you're quick you can take both out, but even if you only take out the Medic, your team can now finish off the previously healed Heavy.
One last tip to playing a Spy - avoid all Pyros! The Pyro class is the Spy's worst enemy and should be avoided at all cost. The flame keeps the Spy from re-cloaking and will kill the Spy in a short time if not removed.
Now get out there and back-stab some Medics and destroy some gun turrets!