Oh boy, Bar Prep practice {chuckle}.
Duty -- Every person has a duty to act as a reasonable and prudent person under the circumstances. This means that the person must do (or refrain from doing) some particular set of actions.For example, a person has a duty to drive with reasonable care, use headlights when they cannot see clearly, pay sufficient attention to the road, not pass when there are oncoming cars or other obstacles blocking the lane, etc.
As part of this, a person has the duty to obey applicable laws, statutes and ordinances. In the example above, the person also has statutory duties to obey the speed limit, maybe to use headlights when it's raining, not pass when there is a double-yellow line, etc. These statutory duties are defined by law, as opposed to the general duties which are defined by 'common sense'.
There are also some special duties, based on circumstances or special relationships, such as the duty of a landlord to a tentant, or fidiciary dutues of a trustee or guardian, or the duty of a common carrier (bus driver, taxi cab operator, etc).
Determination of what duties exist is a question of law.
Breach -- A person breaches their duty when they fail to act in accordance with that duty. This means doing something that the duty requires them not to do, or not doing something that the duty requires them to do. For example, passing across a double-yellow line where there are oncoming cars is both a breach of a statutory duty and of a general duty.
Determination of breach is a question of fact.
Actual Cause -- For a claim of negligence to succeed, the breach must actually be the cause of any harm that results. Actual causation is a question of physics, and is usually analyzed one of two ways, the most common being the "but for" test.
The question is: "but for" the breach, would the event have occurred? For example, if I leave a axe lying on my front yard, and an adult comes along, picks up the axe, and goes across town to kill someone, then 'but for' my leaving the axe there, that axe could not have been used in the murder. If I had duty to not leave axes lying around, and breached that duty by leaving my axe lying around, but for the breach, that victim would not have been killed by my axe.
There's also the issue where two different sources could have been the actual cause. For example, two vice-presidents are out hunting with a third friend. Both shoot and the friend is hit by one bullet. Which vice-president was the one who actually shot the friend? Summers v. Tice is a case that every law student remembers dealing with this situation.
Actual cause is a question of fact.
Proximate Cause -- Just being the actual cause is not enough. Proximate cause also requires that the outcome be a foreseeable (predictable, knowable) result of the breach. For example, if I forget and leave the axe on the front lawn, and during a storm a lightning bolt hits the axe and causes it to fly onto the street hitting a person, there is no way I could have predicted that would likely happen. Hence, the injury was not foreseeable, even though "but for" me leaving the axe there, the event wouldn't have happened. Thus I am not liable. However, if I leave the axe on the lawn, and a child comes along and cuts themself on the sharp edge, that is foreseeable and hence I would be liable (assuming all other elements are met).
The other exception to proximate cause is where there is a deliberate interevening act by someone. In the axe example above, where the adult stole the axe, then went across town to kill someone -- that deliberate intervening act by the axe murderer stops me from being liable for the victim's injuries. Generally, the criminal acts of another person are not considered foreseeable, because we have a reasonable expectation that other people would obey the law, and the courts favor that belief.
The exception to the exception is where we know that a person is likely to commit a criminal (or tortious) act. If I knew my neighbor was a dedicated axe murderer, who practiced axe murdering every Sunday, and that he had run out of axes, and I left my axe on the lawn knowing he could find it, then the outcome would be foreseable.
Proximate cause analysis is a question of law.
Damages -- finally, negligence requires that acutal harm result. Harm can be physical, emotional, monetary, loss of privileges, intereference with rights, etc. However, just the possibility of future harm is not sufficent.
These are the basic elements. There are also lots of weird special case exceptions and variants, and of course the laws of any individual state would be used in an actual lawsuit.