Part of the work in implementing a trust--and which people sometimes do not complete--is the funding or transfer of assets into the new trust. To make the trust properly address the residence, i.e., to govern its ownership and disposition, yes, you do need to transfer the home into the trust. This is a transfer by which John and Mary, husband and wife, or however title is vested, transfer and assign the property to John and Mary, as Trustees, and any Successor Trustee, of the (Name of Trust), dated (date of execution).
This can be done by a quitclaim deed, which assigns into the trust all title that you have and no more; there are no warranties or covenants carrying after-acquired title. A grant deed includes full warranties of title and if you want to be assured that any rights under any applicable title insurance policy are also assigned, that would be an alternative choice.
Make sure that any notices making out exemptions from property tax reappraisal which might apply in your jurisdiction are filed with the deed. You should have a title officer or estate planning attorney check the deed over before you record it.