As playing as the Medic, you heal, make a push with your ubercharge, and watch your surroundings. Because everyone is constantly taking damage, you fill an important role as being one of the keys to victory. Because you can't heal yourself, be sure that you know where the nearest medkits or Dispensers are. Gaining points and having a KDR isn't a priority for a Medic to have. The Medic's goal is to be a force multiplier and take a decent team and make them as godly as you can be!
Unless you are defending yourself or catching up with your teammates, you must always be building an Ubercharge or healing. Even if your teammate already has full overheal, folow him to where the rest of your teammates are. Its dangerous to go alone since you are the biggest target of your enemy team. Any smart player will shoot the Medic first. Many are even willing to use suicide tactics even if it means taking you down for a moment, since you have the ability to erase any damage they have done to your team. Without a constant stream of health, your team becomes vulnerable. Be sure to use your Medi Gun's ability to bend and stretch a distance so you can take the opportunity to hide behind walls or corners, and keep a safe distance when you can so the enemy doesn't get you as easily. Crouching can occasionally help you by making you a smaller target. Watch your back for Spies and other ambushers, too. What contrasts playing Medic from playing Medic well is the ability to avoid taking spam and damage as much as you can while being close to the front lines while knowing your priorities.
Don't only heal one teammate teammate exclusively unless you absolutely have to. Exclusively healing one person only is detrimental to your team since you're not focusing on your most of your teammates. In a competitive setting, such as Highlander or 6v6, a "Pocket" is someone who's primary job is to protect their team's Medic. How will you gain points? For every 600 HP healed, you get 1 point, so there's no need to latch on to one decent teammate to gain points. What matters is that you spread the heals and overheals!
You have to know that you can't heal all of your teammates. You need to sometimes pick who might live and who might die. If you're stuck in a tight spot and you have to pick one person between two people, assuming they're both equally skilled, you'd rather give the Soldier priority over the Sniper. Your healing orders are always changing due to the scenario. When you can, be sure to heal all your teammates and if possible, have someone who can escort you around the map so you can provide aid to your teammates as much as possible. If you can't have one of your teammates protect you, avoid trying to run all the way across the map, but . Your chances of dying will increase significantly and although you may spawn, your Ubercharge won't.
A good Medic will always know where his teammates are located, and since they're always going to take damage, your Medic auto call should be set at 99% health. Also everyone spamming and mashing the E button might get annoying, but in the end this will help you since you're able to know where you can run to in a tight situation. Also if you're able to, remember to communicate with your team so you know where they are.
Be sure to also Spycheck. The easiest way to do that is to walk into a teammate. If you can just walk through them, they're on your side! If you can't walk through them, well... that person is a Spy. Try to get your teammates to kill them, if their hands are too full, you can try to kill them yourself, but be careful! Spies can facestab you due to lag compensation, or sometimes they can land a successful backstab. Even though it can fill your Ubercharge when they're undisguised, its risky to Melee them. Use your syringe gun when you can. Remember that you must always check for Spies, find out if they're using a Dead Ringer, and make sure they're killed as quickly as possible. Any decent Spy will attempt to kill you first no matter what, even though it may cause their possible death. A Medic has to be paranoid about everything.
The only real effective way to deal with a Sniper is to avoid being in his line of sight. That's when its time to get your teammates to have to say where the Sniper is. You can also identify where he's exactly looking at from the team colored dot his rifle has when he's zoomed in. Stay indoors when you can and hide behind buildings and use your environment to your advantage and duck and dance around. When it comes to dodging, and survival, you will learn how to do that over time from game play.
Remember: There is always a Sniper with a scope zoomed in on you or a Spy ready to stab your back. You must also be ready to make snap decisions and judgements. Have your priorities ready, and be organized!
While you're pushing a cart or trying to capture a point, you don't always have to be right on it. You're better off trying to keep distance from your teammates if you can't use them as a meatshield. If there is no enemy threat, feel free to get on the point, but be careful.