Well answers vary depending on where the casualty was/how far the casualty was from the rear/how severe the casualty, etc. So to keep things consistent, I'll use the Normandy Landings as the basis for this answer. Fair warning though, I am not a doctor/medic, so I can't give any advanced information on medical procedures beyond basic terms and practices.

To begin with, let's say you're a rifleman with the 5th Rangers landing on Omaha beach and you're in the third wave to land. You make it far enough to the top of the seawall where you are suddenly wounded by a piece of shrapnel from a German mortar round. Now let's say while you are immobilized by this wound, you are still conscious and aware of the fact that you have been wounded, but you are unable to retreat to seek medical attention or cover safely under your own power.

Obviously, you begin yelling out for a medic (or your squad-mates if they are able or aware). A medic arrives a short time later and quickly assess the situation as he begins basic first aid. It seems that the mortar round was thankfully just short of directly landing on you, however it has managed to take a rather large chunk of flesh out of your right thigh. Your femoral artery thankfully has not been severed, but you are suffering blood loss and will require further medical attention that this medic cannot provide, both due to ability and the current situation. The medic at this point will likely bandage the wound up (to prevent further debris or dirt from getting into the wound and causing infection), make sure you are either somewhat safe where you are for the time being or brought somewhere (either by himself or with the assistance of others) reasonably protective and safe from further enemy fire (and this might not be possible depending on where on the battlefield you are wounded), give you a dose of morphine if he has it and you require it, and then move on to the next wounded man he encounters.

At this point, if the medic has moved you to a safer impromptu triage area, you are likely in with a group of wounded who are being triaged by other medics/corpsman/surgeons (Saving Private Ryan, while not something I would source academically, actually gives you a basic idea of how this works, [here] (http://youtu.be/G6fH4wQPq7U?t=20s) )while awaiting transport back to the fleet. When you are being triaged, the medics/surgeons are actively seeking only to provide medical attention to A)wounded who have a reasonable chance of survival if they receive that attention and B)Need that attention NOW in order to survive. You fall into this group, and a medic and surgeon take turns monitoring your wound, keeping it clean, and providing (limited) medical attention while you await medical transport off the beach. Once you are stable (if at all), you'll be told to sit tight, and they will occasionally check on you periodically to make sure no further action is needed on their part since they will have many others to care for in addition to you.

If you don't fall into those categories, you are either considered walking wounded (able to survive with limited attention and not likely to die of your wounds in the immediate future if they go untreated beyond any first aid you've already received), dead, or considered so far gone that the best anyone can do is maybe provide you with a dose of morphine (if they have it to spare, which may not be the case) to ease your pain and hope that maybe by some small glimmer of hope, you survive long enough to be evacuated from the beachhead.

Now, it's been about an hour after you were first wounded, and the medics/combat surgeons watching over you now have the ability to safely get you off the beach and back to a hospital/hospital ship to receive further medical care. Landing craft that are bringing in further reinforcements to the established beachhead are now utilized as ambulances upon their return to the fleet to bring surviving wounded back to the ships. You are placed upon a Higgins boat and then along with other wounded and possibly a medic to watch over everyone, you're evacuated from the beachhead.

At this point, you are likely going to be put aboard a transport or hospital ship where you can have your wound cleaned and sutured, while you are ferry'd back to England to sit out the next 3-4 months (or less depending on the severity of your wound and the need for empty beds) of the war in a hospital. While there, you will receive further medical treatment and begin recuperation. After you're deemed recuperated, it's possible that you're deemed unfit for combat, and either given an honorable discharge and sent back to the States, or it's decided that you can return to a combat unit or serve in some other non-combat capacity and you're sent on your way.

Keep in mind, this is specific for the Normandy Landings. Though in general, many of the same things would occur if you were wounded in say, Carentan or Monte Casino, though with some obvious differences to how you are evacuated and eventually receive further medical attention (such as being brought from a triage by jeep to a field hospital rather). Feel free to ask any other questions you may have and I'll answer them to the best of my ability!

Sources: Stephen Ambrose's D-Day and Citizen Soldier

Rick Atkinson's The Guns at Last Light