a lot of medic is positioning and game sense so watching demos of both yourself and higher level players is very important. if you're looking to improve your movement try doing jump/surf maps which will help you strafe a lot better. nothing will help you more than actual in-game experience though so play in as many scrims/matches as you can.

Play the other classes and get good at them. This will help you understand the limits of some classes and you might even learn a few tricks to stay alive just a little bit longer. Also ultiduo is fantastic for practicing your surfs, arrows, and Uber milking

scrim medic and pug anything but medic unless you enjoy pugging medic

playing other classes makes you better at medic
edit: rocket jumping is a great way to practice movement in general.

ultiduo and soldier v medic mge

get a degree irl probably

who the fuck would want to do that?

i'd manage to fuck it up

Ultiduo for movement/crossbows
watching invite/prem medics and/or reviewing your own demos

i personally love to surf and thats what i mainly do but soldier vs soldier mge is really good practice for surfing rockets but as everyone else has said you just got to scrim and look at demos either with your team or by yourself. thats the best practice youll ever get.

I wrote a thing but I suck at structure and gave up halfway through so grain of salt

Start off with being as keen as you possibly can. If you _really_ want to improve, you'll find your own way of improving.

Now medic is a very painful and frustrating class to play. You'll get blamed for most things, people will blindly evaluate you and you won't get thanks for a single thing you do. Due to this most players get eaten by the pitfall of excuses, blaming their teammates or retarded opponents for most things that go wrong (even if its not out loud).
I find it very important to remove all emotion from your gameplay. There's always an objective way to look at how you played a situation, and there's always a better way to play the situation. As soon you start blaming people you stop learning.
The most important parts of playing medic in serious 6v6 is positioning and awareness. Some people will tell you dodging, airstrafing or arrowing are what you should improve but those gimmicks are absolutely worthless if you can't keep up with your team and/or get caught out on every occasion.

Go through each point of a map and think about where you want to stay and why. In case you get jumped or rushed, what is the quickest and safest way to get out.
You don't need to figure all that out on your own though thankfully. Watch demos of high level gameplay and try to realize why the medics hold/walk where they do.

It's vital that you pay attention to what is happening around you, whether its the hp of your teammates or possible dangers you need to be as aware of your surroundings as you possibly can. Look for your teammates and realize the situation, check everyone's health and play accordingly. Pay attention to when your players took damage and practice utilizing efficient crithealing.

What helped me a lot was to watch a demo of a top medic in a map I'm about to play or played recently, and compare what they do to what I do. Where they hold to where I hold and who they heal to who I healed.
While you're watching a demo try and write a short point list of what you think went wrong and for the next couple of serious matches, pick one or two things from the list and focus on improving that aspect/skill.
Comms are also an important part of your gameplay, ask if you can spectate on a top level game and listen to how other medics successfully communicate with their team in each situation.

Also, sooner or later if you're serious about getting better you'll find your own way of improving, reading lists from others can only get you so far.

definitely agree with what others have said (esp condom, watching demos and thinking about specific holds and pushes can be super helpful) but i want to emphasize that if you want to get better and medic and play pugs you should try to play other classes as well, as luxor said.
playing medic all the time only gives you one perspective and from a scout or pockets POV for example, you can experience first hand the effect of a good/bad medic if you get dropped in an uber or something like that. Scrims and matches are of course the best way to get experience and practice but watching demos (both of yourself and other good medics as condom said) can help you iron stuff out.
I like to do jump maps cause I feel it helps with movement and muscle memory (did it at i58 to get used to the desk/mousepad even though I was playing scout) but surfing is good for practicing movement/mouse movement if thats what you enjoy

soldier mge

Everyone else has said the main points but a much better option to this ^ is to play degroot keep. It may not be the best practice but has helped my arrows considerably

just practice avoiding or surfing rockets. i find it helpful but not many people like to do it

Demos, practising crossbow and dodging stuff in pubs, more demos

Indust used to do it all the time... like... ALL THE FUCKING TIME.

People have mixed opinions of the dude but he was dodging and surfing better than just about anyone who played back then, and his movement was definitely ahead of its time. Most medics even at the low invite level pretty much ran around randomly and did trashy small up/down surfs back then - and were super easy to kill in comparison.

tl:dr, you'll probably get a lot of shit for it, but med vs soldier mge isn't a bad idea.

Try to main call. main calling is most easily done by medic because you are supposed to the player that's most aware of the current situation (health, position). Work with your team to get information on the enemy's sitation. you will get so much better at the game by directing the flow of it. Even if you tend to make bad calls all the time, it will improve so don't be insecure about making bad calls, not being able to focus on healing (lol), or having an ugly voice or whatever ridiculous excuses medics have for not main calling. I'm not saying that medics should main call in every team, I'm saying that medics should be able to main call, even if they don't do it for the team they are playing in.

The hardest part of playing medic is gamesense, or more specifically, deduction. This is something that you can't get from watching other medics play the game or something that you can learn from playing pugs all day. Learning how to read the game is the most valuable skill you will have as a medic or a main caller. There will be things that are relevant for how you approach a sitation at the time and irrelevant at other times. For example, you are pushing last and the demo just spawned. You don't have to pop through because the threat of dropping your players to a sticky trap is non-existant. You can milk the uber and pop it when you are far inside the last push, and then you had successfully used deduction to understand that there can't be a sticky trap around the corner, which enabled you to get position inside the last point before you popped the uber and consequently won you the round. This is a simple example of deduction, and I can give you many more examples, but at the end of the day it's something you have to learn yourself from getting experience playing the game.

Someone made a map to practise movement, kind of like kz in CS:GO, it applies to every class but I believe it was made with medic in mind.

The sniper class still exists even if their demos dead so probably a good idea to have your teammates watch out for that but I agree with you for the most part. Maybe I'm biased as somebody who plays a lot of pugs (or used to at least) but I feel like playing the 6s in general helps with your ability to read the game. Perhaps it's more helpful to main class and play more serious games at a high level but when you're starting out especially I feel like there's a lot of simple things about the flow of the game to pick up on. It's also pretty easy to main call and tell your team what to do in pugs so that's something to practice as well.
I feel like playing any class so long as you are thinking and don't turn your brain off and run forward blindly can help build awareness and give you a better idea about the flow of the game.
With regards to demos I think it's probably more important to hear comes so if you can find stream vods or YouTube videos of high level medic povs with mumble included. IIRC nursey and shade both have a few on their channel, dunno about any EU meds but I'm sure there are some out there. Not always that helpful because different teams have different playstles so what works for one top player may or may not get you killed because your team doesn't protect you as well or whatever. Always take things with a grain of salt and don't read too much into what others are doing at the end of the day it's what works with your team that is most important.

I mean, playing pugs is better than not playing at all, but pugs also tend to teach you bad habits as medic. In pugs you can get away with having really bad positioning because you're playing against a badly coordinated team, where people are more likely to make nonsensical plays rather than coordinate something that will actually force you or kill you. If you are playing against real teams you get punished for mistakes which normally won't punish you in pugs. The other way around applies to, you play properly in pugs but your team doesn't so you get punished for it. This just makes pugs bad practice, especially for medics. Play pugs to have fun and don't play more pugs than scrims.

I'm pretty sure the map he's talking about is tr_medic.

http://www.teamfortress.tv/27143/tr-medic

This might be a bit of a wierd one but play a few pubs here and there as med as part of your practice. If you want that is. The reason I say that is because as much of a clusterfuck pubs are, as a medic you are forced to rely more on your own judgement of situations and mechanics than your own team to get you out of situations. I say this because I believe a good med can not only function within a team but is also able to function independently and make their own decisions when necessary. However I am not saying don't listen to your teammates as well.

indust