As trustee, you have authority over assets held in the trust—so one of your first jobs as trustee is to figure out just which assets those are. Only property that was legally transferred to the living trust before the deceased person's death can pass under the terms of the trust.
Start with the trust document. It probably lists property that the settlor (the person who set up the trust) at least intended to transfer to the trust. Often, the assets are listed on an attachment to the trust document, called a schedule. It's common to find real estate, bank accounts, and heirlooms in a trust.
Just listing an item on a property schedule, however, doesn't mean that the item is automatically held in the trust. It must be legally transferred. With real estate, that means a new deed, transferring the property from the individual owner to the same person as trustee of the trust. For example, a deed might transfer a house from its owner, Morgan Burke, to "Morgan Burke, Trustee of the Burke Family Revocable Living Trust dated December 21, 2012."
If an asset has a title document, showing who owns it, that document must show that title is held in the name of the trustee (or less often, the trust). So for real estate, it's the deed; for a bank or brokerage account, the account registration; and for a car or other vehicle, the title slip issued by the state. After you check the list of assets in the trust document, look for the title documents to see what was actually transferred to the trust.
For items that don't have title documents—for example, personal belongings or household furnishings—it's usually enough just to list them in the trust document. In some states, however, there needs to be a separate document stating that the items are being held in trust. In New York, for example, there must be an "assignment of property" document, listing assets that are to be held in trust.
Another way to get assets into a trust is to leave them through a "pour-over" will. The idea is that anything that passes through the will is poured straight into the trust, and distributed to the trust beneficiaries. It's a way of catching any assets that were supposed to have been transferred to the trust but weren't. For more, see How a "Pour Over" Will Works.
The executor of the will (who is often the same person named to be trustee of the living trust) transfers the property into the trustee's name. This may or not require a formal probate proceeding; it depends on the value of the property that passes through the will, and state law. Most states allow "small estates" to skip probate altogether or use simplified probate procedures. But what qualifies as a small estate is different in each state.
It's very common for people to forget to transfer property into their living trusts. They sign the trust document and think they're done, or they just never get around to doing all the other paperwork. If there's no pour-over will, the property will probably have to be distributed under the terms of the deceased person's will, not the trust.
In California, however, there's something called a "Heggstad petition"—a request to the court to allow property that was intended to be in the trust to be transferred to the trust. Going this route is expensive (you'll probably have to hire a lawyer) and may not be worth it unless the property is quite valuable.
Keep in mind that many valuable assets don't typically pass by a trust or a will. Some examples include:
Life insurance proceeds. These go to the beneficiary named in the policy documents.
Payable-on-death bank accounts. The funds in these accounts go to the named POD beneficiary.
Retirement accounts. If the account holder named a beneficiary, as most do, that's who inherits the money.
Jointly owned assets. Most joint ownership carries with it the "right of survivorship," which means that the surviving co-owner owns the property. If property is owned in joint tenancy, community property with right of survivorship, or tenancy by the entirety, the survivor automatically owns the property.
Real estate subject to a transfer-on-death deed. More than a dozen states now offer TOD deeds, which let property owners name someone to inherit real estate.