I'm not from the USA, and the current US Constitution is a pretty great one, actually, as these things go. Generally speaking, just strive to replicate its overal approach. But here's some general advice that I'd give to anyone writing a constitution:
1. Define your union as a voluntary one, and explicitly recognise the right to secede from that union. Outline the process for doing so in a legal and peaceful manner. (This requires, at the very least, a pleibiscite; and the right of contiguous areas that oppose secession to countersecede and thus stay with the union when the rest of their state opts to depart.)
2. Strengthen the right to bear arms by altering the phrasing into something like "Neither the federal government nor any government of or within the several states shall infringe in any way upon the right of citizens to bear arms. No law shall be made that restricts, hinders or regulates the right of citizens to own and bear arms in any way whatever."
3. Include a provision that orders the federal, state and local governments to have a balanced budget at all times.
4. Include tight restrictions on public debt. Decree a (modest) percentage of the year before last's GDP to be the upper limit of public debt. Ensure that the government can only go into debt in the case of an acute crisis that existentially threatens the country-- and even then only with a two-thirds supermajority in both houses. Public debt may only be incurred for a fixed number of years out of a given larger number of years (for instance: the government may only incur debt for any five years out of 50, and may not borrow money under any circumstance during the other 45). All debt must be fully paid off within 20 years (no long-term debt, ever; the generation that incurs the debt must also pay it off).
5. Restrict all bills to a single topic that must be accurately described in the title. Also restrict all bills to a maximum word-length. Oh, and make sure there's a line-item veto, so stupid provision can be nixed while the rest of the bill gets adopted.
6. All legislation gets a horizon clause of 20 years, after which it is automatically voided unless explicitly renewed by both houses of Congress. Ensure that there can be no "shortcuts", or "automated renewals". There must be a full vote on every extension. If this is not done, the law is voided thenceforth. Any law that is voided may not be re-introduced for at least five years thereafter, nor may a law effectively containing the same (or suspiciously similar) provisions be introduced.
7. Keep the "neccesary and proper" clause (or similar 'sweeping' phrases) out of the new Constitution. Bolster the principle of subsidiarity by far more explicitly limiting the federal government to certain well-defined core tasks. Everything else is to be handled exclusively by state or local governments. (This will result in the complete abolition of most federal departments and agencies.)
8. Explicitly abolish and forbid the existence of all Federal policing organisations (such as the FBI), with the sole exception of the US Marshals.
9. Stipulate that agencies of the government (at any level) cannot ever have regulatory authority of any kind. All regulations must be adopted through the responsible legislature before they can come into effect.
10. Have the Senate elected by the state legislatures again.
11. Severely limit intellectual property claims. No more "Disney extensions" or bullshit like that. And all non-profit use is automatically fair use and may not be infringed upon in any way whatever. (Disney will never again be able to sue kindergartens for painting Mickey Mouse on the wall.)
12. Severely limit eminent domain. The government should never be able to take your property "just because". The use of eminent domain must be based on clear and undeniable importance to the affected community, and the state must prove in court (before a popular jury, not some judge) that there is no other way. In any case, the valued of the seized property must be appraised independently, and the government must pay at least twice the appraised value. (And that sum multiplies over and over, the longer the property has been in the owner's family.)
13. Generally ensure that not only the federal government, but also state and local governments and any organisation that receives any public funding is to be bound by the Bill of Rights. (Which means, for instance, the universities cannot ever again limit free speech on their campus in any way.)
14. Strictly define citizenship to be based on ius sanguinis, and never on ius soli.
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And some more drastic proposals that I'd also like to put forth, but which I know a lot of people opppose (for some reason or another):
1. Instead of merely limiting public debt, intellectual property and eminent domain (as outlined in points 4, 8 and 9 of my original list), abolish all three completely. Ban public debt for the federal government and for state and local governments. Determine that property rights can only apply to the physical universe, never to the immaterial realm of ideas. And forbid the government from ever unilaterally seizing someone's property. (The ban on public debt also renders most of the provision mandating a balanced budget to be moot.)
2. Limit taxes to tariffs and one direct tax. The tariffs must be based on reciprocity. (If another country lowers or abolishes theirs, you also lower or abolish yours, correspondingly. If they introduce or increase tariffs, you do the same to them.) The direct tax levied upon the citizenry can take any given form (e.g. property tax or income tax), but key is that there can only ever be one tax, and that the citizens must actively transfer the money to the government. It must not be 'kept back' on their pay-ckeck or something. (Why? So that they feel the pain of having to pay far more directly. This demonstrably increases support for keeping taxes low!)
3. The revenue of the direct tax is constitutionally apportioned. So x% goes to the local government, y% goes to the state government, and z% goes to the federal government. (I propose something like 60% local, 30% state, and 10% federal. This, again, works towards subsidiarity and "most things being done locally"... as they should.) But regardless, for each of these allotments, the taxpayer should be able to earmark his own money. That is: he should be free to specify "all of my federal stipend goes to the army, and to nothing else". This is all tallied up when the taxes are paid, and that determines the government budget(s) for the next fiscal year. Governments may not deviate from the instructions the taxpayers give them. (Allowing the taxpayers to effectively form the budget automatically means that the resulting budget is equivalent to the tax revenue; a balanced budget amemendment is now entirely moot.)
4. The direct tax must be explicitly barred from having any loopholes, exceptions, or complexities of any kind. It must be a simple, flat percentage without any further complications whatever.
5. Only those who pay the tax are eligible to vote (or to be elected). Discard any amendment that prohibits this. It is of the utmost importance. No taxation without representation... and no representation without taxation. You don't pay, you don't vote. This prevents a purely parasitical class from having any say in how the country is run.
6. There must be a constitutionally mandated gold standard for the currency, and a universal ban on government-issued fiduciary currency.
7. Add an article that bans the export of gold under all circumstances, and which allows the federal government to determine materials, substances and technologies of vital strategic importance that may not be (freely) exported.
8. Add an article explicitly stating that any action that has no concrete, identifiable victim (other than "yourself") cannot ever be criminalised (at any level of government).
9. Add an article banning the concept of fines paid to the government. If any fines exist, they must be paid out to the victim. (As per the above, acts that have no victim cannot be criminalised anyway.) Under no circumstance should the government financially profit from punishing someone-- that's a perverse incentive.
...I'm sure there's more to be said, but this would be the core of my advice to anyone drafting a new constitution. It's all aimed at thoroughly restraining the power of government, creating a stable economy without "ponzi scheme policies", and forging a "stake-holder republic" where power is held by those who do all the work and pay all the bills.
