Ok, so the Medic is my most played Perk, I have around 350 hours in the game. Im going to give you tips on how I play and keep people alive.
The Medic is used for a supportive-type player that provides the team with a set of movement, damage and resistance buffs. First thing is you dont really want to go for the Medic smg, its unless as of right now. You want to hang onto the Pistol until around wave 3 or 4 if your team hasnt given you any Dosh. Go for the AR if you can afford it, then the medic shotgun.
The Medic AR is the medics bread and butter, it deals good damage and heals like a champ. Each time you heal a teammate with a medic dart it takes 30% of the Dart charge, so you can have a total of 3 darts before the gun has to charge again. For me personally I use the charge time to switch between weapons to have a consecutive barrage of healing darts going at all times. Now at lvl 1 it will take the gun 10 seconds to fully recharge, and goes down 8% every lvl.
The Medic shotgun is also a very good gun, I use it to help clear out zeds that are closing in on teammates when they are distracted. It takes around 12 seconds for it to fully recharge. You can use darts before its fully recharged but not the full amount.
As you know the Medics job is to heal and keep the players alive. This will get challenging on higher difficulties. Players like to split up sometimes and you can be every at once. I usually stick by the most player, if one or two players want to wonder off, dying is their punishment, same goes for you, teamwork is key, stick together. This brings me to another point. Its VERY important that you actually heal, many players who play Medic rarely heal and instead go for kills. Thats a no no, if you want to shoot Zeds go play another Perk, you will level up by healing. So what you want to do is only heal, what I tend to do is constantly heal everyone at all times, teammate has 80% health? Heal, Buddy just got hit by a crawler? Heal. Heal at ALL times, not just when they are about to die, because if you start then your already ****ed. Now thats not to say you cant shoot any Zeds, you want to watch your teammates backs as well, if they have a Clot coming up on their back then kill it. Your a support role so support.
Lastly you want to pick the correct skills. There is a clear right way and a wrong way to picks skills. If you want to be the best medic you can be, you have to pick all left side skills. If you want to solo or be a selfish Medic who only wants kills then pick the Right side. No right side skills has anything to do with actual healing., just weapon damage and reload speed but you dont need those because you'll to be too busy healing. The Left side of the skill tree has everything you need to be a great medic, stuff like speed boosts for your teammates when you hit them with darts, damage resistance and healing yourself when you heal others.
It will take time to perfect the Medic class but stick with it and it will be rewarding and you'll also never want to play another Perk in public lobbies because every other medic is trash. Dont forget you can also heal with your syringe and it will charge faster if you heal a teammate that is dose on yourself.
If you have any question feel free to ask. Hope this helped.