Not sure how basic, or how much detail you'd want, so I'll try to cover most things as I think of them
Medic
One of the most useful team characters in the game. One or two good medics on a team is essential on most maps. Use the secondary weapon to heal players (left mouse button) and just keep healing anyone and everyone, as much as you can. The more people you heal, the more you'll see the 'ubercharge' go up. When the ubercharge reaches the top of the bar, you'll hear it say 'I am charged'. This is where the destruction can begin
Find one of the best players on your team, preferably a heavy, pyro, soldier or demoman. Start healing that player and then use the right mouse button to activate the ubercharge! You are both now invinsible for a short period of time, so you need to make sure that you activate it at just the right point. Activate it too soon and the player you're supporting wont be able to get to the action before it wears off. Especially with a heavy, because they move so slowly, you really need to be just round the corner from the action, so that they just need to pop out and then unleash the fury! With a pyro on uber you can spread mass panic in the other team. Pyro's are reasonably quick and do all their damage close up, when they are protected by uber they just need to get stuck in as close as they can and the other team will scatter, creating plenty of confusion for your teammates to exploit.
The only other thing to focus on, is healing teammates who are on fire. If a group of your teammates gets set on fire, move quickly from one to the other, healing them until they stop burning. Don't worry about healing them fully at first, just get them to stop burning. Once you've saved them from initial danger, then you can go back and heal them all fully.
I tend to try and stay up close to the action, but just tucked out of the way. Use cover (corners of wall, blocks, etc) to make sure you're not in the main fight. So long as you are close enough you can heal your teammates without putting yourself in the firing line.
Engineer
Again another of the most essential team characters. One or two good engineers will make a huge difference to a team. Often the error is to have too many engineers though!
Usually my first step is to set up a teleporter entrance right by the spawn point (press '4' and select Entrance). Then go back into spawn and go to the medi-cupboard to get more 'metal?' (whatever it is you need to build with)
The next thing to do is to pick a safe place just behind the main action. Put up a 'dispencer'. This is used to heal anyone on your team who walks up to it and also importantly for you, used for re-stocking 'metal' supplies.
Next you'll probably want to build a 'Sentry'. Build this somewhere near your 'Dispencer' but pick a spot where it will only be attacked from one direction. Try to make sure that its got a good line of sight to where players will be emerging from a corner or doorway. Use your 'wrench' to hit the sentry and this will upgrade it with your 'metal'. Keep going back to your dispencer to re-stock your metal when it runs out (this is why you want the dispencer build near-by, usually just round the corner out of sight). Keep upgrading the Sentry until it can't be upgraded any further.
The next thing to remember is to build an 'Exit' for the teleporter you set up earlier. This is one of the most important parts to the game on bigger maps. It gives your team a huge advantage, as when they die, they can get back to the action so much quicker! Many engineers forget about it, and tbh they are contributing so much less to the team if they don't build this.
I tend to stay close to my buildings as an Engineer for two reasons. The first being that you need to 'repair' them (hit them with your wrench) if they get attacked and damaged. The second, and often the most annoying, is if a Spy manages to sabotage them. You'll get a warning whenever any of your buildings are attacked or sabotaged by a Spy. Especially with the Spy attack, you need to get to them quickly and hit them a couple of times with your wrench to prevent them from being destroyed. If the other team has good spys, I often try to get a pyro on my team to stay reasonably close to the main turrets and dispencers, as pyros are perfect for flushing out any spys!
On big maps, you'll probably end up destroying your own buildings (press '5' and select from there) so that you can move them up to keep up with the action. It is really important to pick the right time to do this, and totally depends on the map. Leaving your buildings too far back from the main fight, just means that they're being wasted. Trying to move them too soon, means that they'll probably get destroyed while you try to build them. I tend to move the dispencer first, because you'll need to use this to re-stock 'metal' at your new build point. Then get your Sentry moved up to somewhere nearby and upgrade it as before. Finally, and most importantly, get that Exit moved up, to keep your teammates right in the action!
Can't think of much else I'm afraid - but certainly two very useful characters to spend time improving
. Also medic is the least played class according to the stats: 