You must be competent and of legal age to make a valid will. If you are underage -- under 18 in most states -- the court distributes your property according to your state's intestate laws regardless of whether you write a will. The courts consider you competent -- also termed "of sound mind" or "having testamentary capacity" -- if you understand that you are making a will that will distribute your property at your death. Neither eccentricities nor drug or alcohol use render you incompetent as long as you have testamentary capacity at the time you sign the will.
Execution of a will means the will-signing procedure required by your state. In most states, probate laws regulate the execution of your will much more than the substance. You can likely leave your entire estate to your pet turtle without running afoul of the law, but if you neglect the witnessing requirements, your will is invalid. All states require that you sign your will before at least two of-age witnesses, and many require impartial witnesses -- people not named as heirs under your will. States impose different execution requirements for other types of wills, such as international wills or holographic wills.
In order for your will to be valid, it must express your intentions for the distribution of your property, not somebody else's intentions. When heirs challenge a will claiming undue influence, fraud or mistake, they are essentially claiming that the will does not represent your free choices. Undue influence means that someone in a confidential position improperly pressured you into making or omitting devises. Fraud means that someone tricked you, and mistake means that you were ignorant of critical facts when you wrote the will, not knowing, for example, of the existence of a new grandchild.
You can freely change or revoke a last will and testament during your lifetime, and the courts will not enforce a revoked will. A new provision (termed "codicil") added to a will alters or eliminates a bequest, and a new will supersedes the old. It is also effective revocation to state that you revoke the will, then to take some step toward destroying the will, like tearing it up or burning it.