1: Predict where the target will move. Put your cursor there, and when his head is in the crosshairs, fire. This way you won't have to follow their heads everywhere they go.
2: Know that you will not hit them every time. There will be misses. And blood because of it.
3: Keep moving, Especially against enemy snipers. The more you move, the less the enemy has a chance of hitting you. Except for crockets, then you're basically screwed.
4: Be an attentive listener. This is helpful when a spy just happens to decloak out of nowhere behind you. It help to spy check everyone you meet, too. If you listen close enough, you can even hear the direction shots are coming from, so you will be ready to shoot whoever comes out of hiding.
5: Noscope when the enemy is at medium-close range. It's still perfectly accurate, just not charged. Scoping and unscoping takes too much time. In these cases, go for the bodyshot to dish out damage, for you will most likely miss the headshot, and if you do, it is almost guaranteed not to kill them.
Onofficial tip: Run like the dickens from the Pyro. Like almost every other class, they are your bane up close.