The institutions that manage your financial assets - banks, mutual fund companies, brokerage firms, insurance companies, etc. - identify you as the legal owner of the assets you have with them.
When you create a revocable trust, ownership of your assets must be officially changed on the institution's records to reflect your trust. You must contact each institution directly to change the legal owner. They will have their own forms and process that they require you to follow to change the ownership.
For information regarding funding specific types of assets correctly into your trust, see here: Funding