Yep most of it is just practice like the others said, but I also think there's an element of confidence/perseverence involved. Sticking with it and having the confidence to know you can improve or be as good helps a lot, although its somewhat harder if this is your first FPS. For me I hadn't played any FPS hardcore in a while since SoF2/PlanetSide (a bit of CS:S inbetween) so I had to get back into "game" shape but I had a frame of reference to make it easier to get back there.
For a first-timer its going to be harder since it probably seems some people are doing the impossible. Its really not though and what you should do is try to simplify things before you go for the more difficult. I posted a few tips for someone who was pretty new to FPS in a different thread, but he also had the disadvantage of never using WASD in the past.
First, find a weapon you like. M4 or MP5 are excellent choices as they're full-auto and easy to use. M16 is also excellent although its burst-fire. LMGs are also good for beginners since they've got a fast RoF and a big clip. Key is to get used to the controls first, work on target recognition and firing and hitting a fixed position. If you're dying quickly don't be afraid to waste some ammo. If you know a guy is hiding behind a wall and may pop out, or there's bad guys flashing in and out of a hallway, fire in bursts before you see them. With any game, whether you're a vet or newb there's a learning curve when it comes to weapon mechanics and feedback if you're hitting or missing.
A few tips would be to go into an empty server and just move around. Point out a fixed position (maybe a small object/pixel in the distance) and fire on it. Displace, re-acquire target and hit it again. Displace/spin, go prone or crouch, then fire. Then work on firing and moving at the same time.
As you get better, "advanced" movements/techniques will become second nature and you'll do them subconsciously. When you can jump/strafe/fire and adjust to a moving target (ie your brain compensates for your movement and a target's movement subconsciously) you'll start to see yourself winning those 1v1s.
In live-action servers, again start simple. Minimize your movement and exposure to enemy fire. Try defending fixed strategic positions (camp) and getting the drop on other people first. Crouched or Prone (I don't like Prone personally, too stationary and vulnerable) with sights up and work on your aim and finishing skills (most weapons require more than 1 clean hit). Once you start getting better you can venture out and go for those constant action twitch killing sprees.
Anyways, hope that helps. With a positive mindset and practice, all that's left is the twitch abilities of moving a mouse cursor and your fingers. Some will always have the edge in that department, but that won't stop you from being a good player.