Some have suggested reading Lopez. I further suggest going back to the writing of the Constitution and its ratification for its original intent.
First, to best understand the Necessary and Proper Clause, it is helpful to read Federalist # 33 in its entirety. Here is the beginning of this Paper by Hamilton:
THE residue of the argument against the provisions of the Constitution in respect to taxation is ingrafted upon the following clause. The last clause of the eighth section of the first article of the plan under consideration authorizes the national legislature "to make all laws which shall be NECESSARY and PROPER for carrying into execution THE POWERS by that Constitution vested in the government of the United States, or in any department or officer thereof"; and the second clause of the sixth article declares, "that the Constitution and the laws of the United States made IN PURSUANCE THEREOF, and the treaties made by their authority shall be the SUPREME LAW of the land, any thing in the constitution or laws of any State to the contrary notwithstanding."
These two clauses have been the source of much virulent invective and petulant declamation against the proposed Constitution. They have been held up to the people in all the exaggerated colors of misrepresentation as the pernicious engines by which their local governments were to be destroyed and their liberties exterminated; as the hideous monster whose devouring jaws would spare neither sex nor age, nor high nor low, nor sacred nor profane; and yet, strange as it may appear, after all this clamor, to those who may not have happened to contemplate them in the same light, it may be affirmed with perfect confidence that the constitutional operation of the intended government would be precisely the same, if these clauses were entirely obliterated, as if they were repeated in every article. They are only declaratory of a truth which would have resulted by necessary and unavoidable implication from the very act of constituting a federal government, and vesting it with certain specified powers. This is so clear a proposition, that moderation itself can scarcely listen to the railings which have been so copiously vented against this part of the plan, without emotions that disturb its equanimity.
Then take a look at what Madison said in Federalist # 44:
The SIXTH and last class consists of the several powers and provisions by which efficacy is given to all the rest. 1. Of these the first is, the "power to make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this Constitution in the government of the United States, or in any department or officer thereof. "Few parts of the Constitution have been assailed with more intemperance than this; yet on a fair investigation of it, no part can appear more completely invulnerable. Without the SUBSTANCE of this power, the whole Constitution would be a dead letter. Those who object to the article, therefore, as a part of the Constitution, can only mean that the FORM of the provision is improper. But have they considered whether a better form could have been substituted? There are four other possible methods which the Constitution might have taken on this subject. They might have copied the second article of the existing Confederation, which would have prohibited the exercise of any power not EXPRESSLY delegated; they might have attempted a positive enumeration of the powers comprehended under the general terms "necessary and proper"; they might have attempted a negative enumeration of them, by specifying the powers excepted from the general definition; they might have been altogether silent on the subject, leaving these necessary and proper powers to construction and inference. Had the convention taken the first method of adopting the second article of Confederation, it is evident that the new Congress would be continually exposed, as their predecessors have been, to the alternative of construing the term "EXPRESSLY" with so much rigor, as to disarm the government of all real authority whatever, or with so much latitude as to destroy altogether the force of the restriction.
It would be easy to show, if it were necessary, that no important power, delegated by the articles of Confederation, has been or can be executed by Congress, without recurring more or less to the doctrine of CONSTRUCTION or IMPLICATION. As the powers delegated under the new system are more extensive, the government which is to administer it would find itself still more distressed with the alternative of betraying the public interests by doing nothing, or of violating the Constitution by exercising powers indispensably necessary and proper, but, at the same time, not EXPRESSLY granted. Had the convention attempted a positive enumeration of the powers necessary and proper for carrying their other powers into effect, the attempt would have involved a complete digest of laws on every subject to which the Constitution relates; accommodated too, not only to the existing state of things, but to all the possible changes which futurity may produce; for in every new application of a general power, the PARTICULAR POWERS, which are the means of attaining the OBJECT of the general power, must always necessarily vary with that object, and be often properly varied whilst the object remains the same.
Had they attempted to enumerate the particular powers or means not necessary or proper for carrying the general powers into execution, the task would have been no less chimerical; and would have been liable to this further objection, that every defect in the enumeration would have been equivalent to a positive grant of authority. If, to avoid this consequence, they had attempted a partial enumeration of the exceptions, and described the residue by the general terms, NOT NECESSARY OR PROPER, it must have happened that the enumeration would comprehend a few of the excepted powers only; that these would be such as would be least likely to be assumed or tolerated, because the enumeration would of course select such as would be least necessary or proper; and that the unnecessary and improper powers included in the residuum, would be less forcibly excepted, than if no partial enumeration had been made. Had the Constitution been silent on this head, there can be no doubt that all the particular powers requisite as means of executing the general powers would have resulted to the government, by unavoidable implication. No axiom is more clearly established in law, or in reason, than that wherever the end is required, the means are authorized; wherever a general power to do a thing is given, every particular power necessary for doing it is included. Had this last method, therefore, been pursued by the convention, every objection now urged against their plan would remain in all its plausibility; and the real inconvenience would be incurred of not removing a pretext which may be seized on critical occasions for drawing into question the essential powers of the Union. If it be asked what is to be the consequence, in case the Congress shall misconstrue this part of the Constitution, and exercise powers not warranted by its true meaning, I answer, the same as if they should misconstrue or enlarge any other power vested in them; as if the general power had been reduced to particulars, and any one of these were to be violated; the same, in short, as if the State legislatures should violate the irrespective constitutional authorities. In the first instance, the success of the usurpation will depend on the executive and judiciary departments, which are to expound and give effect to the legislative acts; and in the last resort a remedy must be obtained from the people who can, by the election of more faithful representatives, annul the acts of the usurpers. The truth is, that this ultimate redress may be more confided in against unconstitutional acts of the federal than of the State legislatures, for this plain reason, that as every such act of the former will be an invasion of the rights of the latter, these will be ever ready to mark the innovation, to sound the alarm to the people, and to exert their local influence in effecting a change of federal representatives.
What was said on this topic in the Ratification Debates of the States? More to come.