Starting out, the medic is probably the least-flexible and least-equipped of all the classes in Enemy Territory. You start with a Thompson (MP40 if Axis) with a single clip of ammo, a grenade, 8 syringes, and the health pack. So it should be fairly obvious that at least initially, a medic is not a front-line fighter. Their primary strength lies with keeping the rest of their team combat-ready, and their syringes even allow them to revive the recently-killed on the field of battle.
The two unique abilities of the medic are the health pack and syringe. The health pack drops a kit which provides 20 points of health, and initially requires a quarter of the medic's power bar to use. When level 2 first aid is reached the health packs require only 15% of the power bar, allowing the medic to heal a much larger amount in the same amount of time.
The syringe, on the other hand, can actually be used to revive the dead. When a comrade is killed, a red icon will appear above their body. While the syringe icon is there, they can be revived by selecting the syringe, standing over the teammate, and pressing fire. Note that the icon will disappear if the player enters the respawn queue or takes too much damage, so get to them as quickly as you can. You can also see the syringe icon on the compass in the corner of the screen if you're close enough, so you can use it to locate fallen allies quickly.
A good medic will find themselves in the line of fire quite often, but they should never be the first line of an assault. Instead, it's better to hang back, wait for the first wave of soldiers to engage the enemy, and then run in with a needle to raise the fallen and health packs to revitalize the wounded. Charging into the middle of a firefight with nothing but a syringe in hand is risky, but can easily turn the tide of a close battle while earning valuable experience. Just remember that a medic is no good to their team dead, so don't hesitate to heal yourself when you need it.
A medic can expect to gain experience, and thus ranks, very quickly on the front lines of combat. First aid is probably the first improvement you'll see, and one of the most important. The benefits are another clip and grenade, decreased power cost for health packs, full revive for teammates, and finally the adrenaline syringe. These will greatly decrease your dependence on lieutenants, and allow you to heal your team much faster. The last bears special mention - it gives you 10 seconds of adrenaline, during which your stamina bar will not decrease and you take only half damage from all attacks. Obviously, being able to run into and out of heavily defended positions can be incredibly useful at the right times. Battle sense and light weapons are the other areas medics are likely to improve in, and all of the light weapon abilities are useful... especially the extra clip given at level 1. Battle sense gives great benefits at level 2 by recharging your stamina bar faster, and at level 3 by increasing your health by an additional 15.
Finally, remember that the power of a lone medic should not be overlooked. Their ability to heal themselves, when coupled with their innate regeneration, makes them excellent for defending a position by themselves when necessary. A medic behind the barrel of an MG42 can often hold off an entire team for some time by healing themselves when necessary.
So here's the lowdown on first aid, the medic's special ability. This is cropped from the manual - you can read the whole thing by checking in the Wolfenstein: Enemy Territory program group.
This is a Medic-specific skill that rewards players for reviving team-mates and healing them with Health Packs. Medics earn 1XP each time they heal someone with a Health Pack and 4XP every time they revive another player with their Syringe.
First Aid Level 1: Medic Ammo
Medics receive an extra ammunition clip and grenade with their basic weapon load-out.
First Aid Level 2: Improved Resources
2 syringes extra max ammo, 2 extra on spawn plus Medic pack only takes 15% Power Bar instead of 25%
First Aid Level 3: Full Revive
Syringes now return fallen team-mates to full health.
First Aid Level 4: Adrenalin Self
To equip the adrenalin shot press the Special Weapon 1 key (5 by default) twice and then press the primary fire key to inject the Adrenaline syringe. Doing so will impart a temporary bonus in Health and Stamina. For 10 seconds you will only suffer half damage from any attack and your Stamina Bar will not decrease at all, even if you are sprinting. This will give you the ability to rush into and out of strongly defended areas which may prove of critical tactical importance.