A trust is an arrangement between three entities - the grantor (or settlor), the trustee, and the beneficiary.
The process is initiated by the grantor - the individual who wishes to give away assets by placing them in a trust. The grantor places the responsibility for those assets in the hands of the trustee.
The trustee is accountable for ensuring that the assets are received by the beneficiary in the manner intended by the grantor, which is outlined in the trust document.
Here is where it can get interesting - in some cases, the grantor and the trustee may be the same individual. So, a person can say “I no longer own this property for myself, I now own it only to take care of it for a beneficiary.”
Even more interestingly, the grantor may also be the beneficiary, as in "I will direct myself to only use this property in this manner". A layer of law fixes a trust in place, and there can be tax implications.
Typically, a trustee is a trusted person or persons, or a trusted institution such as a bank.