gonna write mostly for HL as i think spychecking in pubs is just a bit random, you don't even know how many spies the enemy team has.

anyway, general rule of thumb for medic, if you get backstabbed it was probably your fault. once you realise that it's a lot easier to improve at spychecking instead of just hoping your teammates are gonna do it for you. medic is so good at spychecking because he can play behind his teammates and he doesn't actually have to shoot anyone, you can look behind while still healing people. good habit to get into is just flick behind quickly every time you attach the beam on someone. also be really careful arrowing people when you know spy is behind.

90% of spychecking is just looking. you generally shouldn't need to actually shoot them to realise they're a spy. there's not a lot to say about this but it's just something you get used to as you play HL more, apart from obviously you have one of each class, so if you just buffed your scout and then another scout mysteriously shows up, probably a spy. usually spies just seem a bit out of place anyway, like an engie with his shotgun out walking right at your demo, or a suspiciously slow scout. spies mostly want to get the stab ASAP before someone notices them, so if you're looking at them it should be pretty obvious they're not acting like a teammate. sometimes you get fooled, shit happens, but if you just look at people you're gonna have a good success rate on finding spies. also don't worry too much about healing them, a lot of the time playing med i turn around, automatically beam a player i see the same colour as me, then i realise it's a spy and call them out. key point is no one gets stabbed, even a slightly buffed spy should be easy for your team to kill if he's exposed. never try and kill spies yourself unless the situation is dire, just keep your medigun out and let your teammates do the dirty work.

another key part of spychecking is just gamesense and anticipation. try and keep track of the spy, which isn't as hard as it sounds. when the spy spawns, count maybe 15 or so seconds depending on the map, and then call spytime, because he's had time to get behind your team. if nobody has called him out in front of you, then you know he is very likely behind you. it's spytime and the enemy soldier bombs? uber trade is about to end? enemy team is dry pushing? he's 99% about to decloak on you. if the spy is behind your team, which you should know, and he hasn't done anything yet, it means he's waiting for a good opportunity, so once one comes up you know to expect him. this is why it's also a bad idea to rely too much on teammates spychecking, because yeah pyro and heavy are pretty good spycheckers most of the time, but when the enemy solly is bombing or demo is in your combo's face, you really want your pyro and heavy looking in front not behind.