the person you sued has a nice job and a beautiful home, but he put
all his savings in a trust. Does that mean the law can't garnish his
money, or can trusts be both discovered (I've heard that some people
have secret trusts) and garnished?
A trust for your own benefit funded with your own money is called a self-settled trust.
First of all, the most common form of self-settled trust, a revocable trust, provides no asset protection at all (these trusts are will substitutes which are used to avoid probate proceedings). Similarly, a trust from which a beneficiary has an unqualified right to remove assets for any purpose the beneficiary chooses (called a "general power of appointment") provides no asset protection against a judgment creditor to the extent of the assets subject to the general power of appointment.
Second, in many states (probably most), self-settled trusts are essentially void as a matter of law as a means to protect assets from creditors of the settlor of the self-settled trust (a settlor is the person who funds a trust).
Even in states where self-settled trusts can bar creditors, a transfer to an asset protection trust is usually going to be what is called a "fraudulent transfer" under the version of the Uniform Fraudulent Transfer Act enacted in state law, which allows the transfers to the trust to be unwound if a lawsuit to do so is filed within the statute of limitations (sometimes four years from the transfer of an asset to the trust, and sometimes four years from the discovery of the transfer of the asset to the trust). Recovery of a fraudulent transfer from a trust is sometimes called a "clawback" of that asset.
In contrast, trusts created by third-parties with assets earned by the third-parties and not derived from the trust beneficiary (e.g. in connection with an inheritance) are generally effective against creditor's claims. This is basically based upon the theory that the donor of the funds could have declined to give the beneficiary anything, and that if the donor of the funds had done so, the judgment creditor wouldn't have had any rights to the funds.
Similarly, if the judgment debtor doesn't have any ownership interest in the beautiful home where the judgment debtor lives (perhaps because it is owned by, and was paid for by, the judgment debtor's independently wealthy spouse or parents or grandparents), the judgment creditor can't seize the house to pay the debt, just because the judgment debtor lives there.
The salary of the judgment debtor is also subject to garnishment (typically 20% of the amount by which the judgment debtor's salary exceeds minimum wage, although there are exceptions, nuances, and complications involved in applying this rule). And, unspent income that is put in a bank account or other asset of a kind that is not exempt from creditor's claims can also be seized.
And, if the judge believes that a judgment debtor actually has a de facto ability to cause the trust to make payments to the judgment debtor and is simply refusing to do so, the judge can hold the judgment debtor in contempt of court. In other words, the judge can throw the judgment debtor in jail until the judgment debtor coughs up the money. There are examples of judgment debtors being held in jail for as long as a decade in these circumstances.
On balance, self-settled trusts are ill-advised forms of asset protection.
Other tools, like fully funding retirement plans, buying large dollar value liability insurance policies, and buying an expensive home in a state with an unlimited dollar amount homestead exemption (like Texas), are far more effective. Certain other assets are also exempt from creditor's claims, although the exact list varies from state to state, and the value of the assets that can be shield from creditors by through ownership of these assets is usually modest. (To be clear, these are only examples. This isn't an exhaustive survey of all possible ways to protect assets from one's future creditors or to discourage creditors from trying to take an asset in payment of their claims.)
There are also certain debts and legal tests (e.g. securities fraud, child support, embezzlement from a trust fund, and Medicaid eligibility) that receive special treatment compared to the kinds of debts used as examples in the question and also compared to plain vanilla breach of contract debts (like unpaid credit card debts or money owed on a business loan or unpaid rent).
Not disclosing the existence of a secret trust in the face of interrogatories (written questions) directed at a judgment debtor from a judgment creditor, or in a deposition of a judgment debtor regarding the judgment debtor's assets, is a serious crime that can result in incarceration for perjury, serious contempt of court sanctions, and more. No legitimate asset protection trust attorney ever recommends that a judgment debtor lie about the existence of an asset protection trust. An attorney that did would be disbarred.
Of course, people lie about the existence of assets that could be used to pay their creditor's claims in the face of debtor's interrogatories or debtor's depositions all the time (often in cases far less sophisticated than secret trusts, like cash or gold bars buried in a box in their garden). Sometimes they don't get caught. But this doesn't make it legal to do so.