This goes without saying, but as a Spy, act like you're part of the other team.
Try to avoid running towards the opposing team uncloaked.
Plan out your strategy beforehand. Pick a disguise, use it, then un-disguise. Then when you're ready to sneak in, cloak, hit 'B' (uses last disguise) and sneak behind the lines
Snipers are good Spy fodder. So are Heavy/Medic combos.
Don't cloak immediately after teleporting, as you will leave a trail and be spotted easily.
Pyro's are your bane.
Try not to stab people when enemies can see you do it.
You can't cap a point while disguised/cloaked, and the instant you pick up the intel you un-disguise.
Engineers are like fish in a barrel. Disguise, sap the turret, hit 'Q' to switch to your last weapon (knife) and stab the engy before he even knows his sentry was sapped. Alternatively, you can stab the engineer when he's behind his gun, and hit 'Q' fast enough to switch to your sapper and sap the turret after the engy is dead, but before the turret has turned around to you. If he's really close to his gun you can sap through him as well.
Mostly basic stuff, but hopefully some of it is useful.