Spying in competitive games is quite a lot harder than doing the same on a public server. The Spy capitalizes on his enemy’s mistakes to be effective. However, a well-organized competitive team makes few mistakes, so Spy makes for a very, very difficult playing experience.
For one, you absolutely have to be good with your revolver. Standard competitive classes move quite quickly, and so they can be tricky to stab. At the same time, two or three well-aimed revolver shots can significantly reduce an enemy’s health, allowing the rest of your team to pick them off (or, if they’re at low health, crediting you with the kill). Good aim is critical.
Disguise-wise, you don’t have many choices. Demoman’s a good bet, as is Medic (acting like a Medic but refusing to “heal” enemies is a great way to get them to start shouting over voice com). Change disguises frequently and make sure your choice of disguise fits the situation. Check your scoreboard a lot – if you know which enemy players are playing which classes, you can see if they’re dead or alive and choose your disguise accordingly.
When disguised, you can see enemy players’ health. If an enemy player’s health is low (particularly the Medic), call it out to your team, and if you’re feeling adventurous, try to take him/her down with a well-placed revolver blast. And check your scoreboard! Try to take out high-scoring players if you can. While the Scouts are nearly impossible to hit with the knife (unless you’re incredibly good), Soldiers and Demomen can be fine targets. As with a public server, they usually make easy pickings if they’re distracted by your team. Careful, though, because they’ll call your position to their team immediately. Solitary players (such as the enemy long-leash Soldier) are usually safer to kill than the combo. If an enemy is protected by Scouts, it’s generally best to back off and try again another time.
Nevertheless, the Spy is incredibly hard to pull off in a competitive setting, especially as a match progresses. I hate to say it, but in ninety-nine percent of cases, you’ll be better off as a Scout.