Practice, practice, practice.

As much fun as it may seem do not start with a Sniper, for me at least, everyone else who snipes will be better than you and can peg you from across the map. I think playing as the Pyro and the Soldier is fun to charge in and relatively easy to get kills. Scout is just damn fun to play even if you don't get kills. Medic is good for a team but a bit boring. Engineers can be boring but primely placed turrets can rack up kills. I never really play as the Demo or the Heavy so I wouldn't be able to tell you. The Spy is really hard to play as so people tell me so I would not start as that class. I would recommend trying to find larger games so when you die (and you will die a lot) it won't affect your team as adversely as it would in a smaller game. 

Try pyro and heavy.

engineers pwn

depends on what class you want to play  
1. scout : Its pretty hard to play and u will need to have a totaly lag free computer to really master it but with some training u will make it 
2. spy : google omgninja spy tutorial 
3. Sniper: just aim for the headshoots :P good training map cp_orange 
  
I play these 3 mostly and if u just wanna get some kills then play as the nr.1 noob class of all times pyro u just run straight forward on any map and hold the trigger button down :P

Find a big game of Capture Point or Payload. Cause it won't matter if you die a million times and you'll respawn quickly. Don't do Arena as you'll won't respawn and have to wait the entire round only to probably get killed quickly again in the next.
 
Which role you should take depends highly on your playing style. Try them all out and see which you like most.

I personally started out as a medic, this can be fun if you find a good Heavy player. Though you won't do much killing yourself, so that can get boring.
 
Heavy is also good, slow but strong.
 
Scout  is fast, personally I find the scout more fun with the bat that allows you to shoot balls but you
 
Spy is DIFFICULT, you'll need to know the maps and how people tend to go around to be a good spy.
 
Pyro is fun as you get up and close in the battle and light people on fire! Accuracy isn't that important either.
 
Demo, you'll need a bit of time to learn how to properly aim and to see how the grenades react. Know that you can do massive damage if the circumstances are right. I once took out 8 people at once, cause they were all hugging around a dispenser.
 
Soldier, can be fun I personally never learned how to shoot those darn rockets properly.
 
Engineer, tends to be a bit boring, cause you'll spend a lot of time building and waiting for stuff to happen.  Though you can be a real asset to the team. Similar to the medic.
 
Sniper, difficult to master fun to play.

Medic is a great class to begin with.
Your job isn't too hard to fulfill, but most importantly, you can observe what your teammates do and learn from them.

TF2 Wiki has some pretty in-depth tips on the Scout, Soldier, Pyro, Demoman, Heavy, Engineer, Medic, Sniper and Spy.

The best advice I can give is to not listen to any advice.
 
I tried forever to look for some secret information I wasn't privy too. Truth is though, it doesn't exsist. The only thing that helps you out there is experience. Find a class and stick with it, eventually you'll get good with it and either move on to a different class or master your already developed abilities. Everything: strategies, map knowledge, class weaknesses and strengths; comes from experience. Sure you can read up on it, but you aren't going to understand how to take down a Pyro as a Soldier until you've done it again and again and again.
 
Oh yes, you'll die. A lot I might add. However that's the price you pay for being new. If we went easy on ya, you wouldn't learn the lessons you need to when it comes time to shine.
 
If you do take any advice away from this topic, let it be this. Whether you realize it or not you are intergral to your team's sucess. You aren't going to take down the enitre enemy base by yourself, you probably won't even be able to make a dent in it. Defense is important, as is taking out key targets like Medics and Engineers setting up near your spawn. If you do use the Wikis and guides, use them to find your prey. Start small and work your way up, and eventually you'll be kicking arse with the best of them.

Practice, and Practice, and Sandvich.
And Don't Die.

I got it on the 360 and here are my tips. 
   
     1. Don't get addicted to the engineer. It is easy to get addicted to the engineer because of his easy turret kills 
     2. Master more than one class. Play as multiple classes so you can be an all around good player. 
     3. Master counter classing. practice killing scouts (damn scouts) and be sure to practice your melee skills 
     4. Team work. Stay close to medics and palce dispensers wisely also stay out of heavys way and leave the sniping to the masters (not me I suck)  
 
Have fun hope this helped.

DrJustice (Team Druidz, Professional Top5 Demomen in TF2)

Reptile (Teamless Currently, Professional, Top 5 Everything)

Auto-Aim (Various People, Professional / Semi-Professional, Top 1 - 10 Players)

Use the Pyro and hold Mouse 1 + W.

Gather some friends and work together. Each class plays differently, just find one that you like and practice with that guy.

Well, why do you suck?

Follow this video 
 
 

Look up "Baron's pub" in the steam groups. It'll give you a list of servers which are great to play on and the regulars are really nice.
 
Youtube videos are very good as everyone has said. Keep in mind though that TF2 gets major updates every few months which change some of the tactics, because of new weapons and class balancing, so not all tactics will still be valid.
 
#1 tip: learn how to spot spies. Mainly..look behind you every few seconds and keep your back to a wall when stationary. There is no FF, so shoot everyone to make sure they are not a spy. They will bleed if  
they are a spy. 
 
 There isn't much advice I can give you without going into detail. Each class plays differently and thus needs its own writeup. Just try each one out and see which one you like the best. When you unlock the new guns, try it out and see if you like that class any better now.
 
I started out as a soldier. That was a long time ago but it might be a good beginning class. Or try engineer and watch what other players do for a bit, or even a medic. Can never have too many medics.
 
Just don't be afraid to die. It's deathmatch, no need to constantly shoot around a corner. You're gonna die...face it.
 
@jonoy52 said:

 1. scout : Its pretty hard to play and u will need to have a totaly lag free computer to really master it but with some training u will make it 

Get good at switching (by 1, 2, and 3) your weapons and learn what the ranges are for each one. Beginners don't tend to understand that melee gets a crit about 1/4th of the time, so it's well worth your while to start punching once someone's all up in your face. 
 
Also, did you know: you can tell from the audio cue whether a sentry is 1st, 2nd, or 3rd level. It's a faint 'beep' or 'beep-beep' (for level 2) or 'beep-beep-beep' (lvl 3).  
 
And if you play Engi, don't babysit your stuff. Get your shotgun out and go earn your extra metal with kills. Your sentry can mop up whatever you don't finish.

Try medic+heavy.  Here's a video of my bro playing that way with one of his friends... kind of ruined a pub game though.

Uber the Sniper as often as you can.

Avoid playing scouts, spys and demos, sniping can be easy, also heavies, soldiers and pyros don't require much skill.

It just comes down to practice. You're not gonna have an easy time around all the vets who have been playing for the past few years. I suggest going Pyro or Medic in the beginning, but just experiment. Just don't stick to one class, try to master as many as you can.

" Remember, when playing as Sniper, ALWAYS bodyshot.  I cannot stress this enough, do it for awhile and you will find out why. "

Attack the giant enemy crabs weak point for massive damage.

I heard GiantBomb.com has a lot of cool tips for the game. 
 
(I've spent hours and hours on the character pages so I'm hoping it doesn't go to waste)

" I heard GiantBomb.com has a lot of cool tips for the game.  (I've spent hours and hours on the character pages so I'm hoping it doesn't go to waste) "