Yes, the constitution can be amended. In fact the second amendment is just that: an amendment. You can continue to add new amendments, even on existing amendments.
This has actually already happened. The 18th amendment established Prohibition. After a short time the 18th amendment was repealed by the 21st amendment. So it is entirely possible to create a new amendment that says
The second amendment is hereby repealed and replaced with .....
The process for this is defined by Article V of the constitution.
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
In simple terms, if 2/3rds of each house of Congress (or 2/3rds of the states) agree then they can propose an amendment. That amendment would then have to be ratified by 75% of the state legislatures. Then the proposal becomes an amendment to the US Constitution.