Examine the trust deed to find procedures for replacing the trustee. If the trust deed includes such procedures, follow them.
Contact all trust beneficiaries and obtain their consent to the amendment of the trust to remove the trustee. This may be ineffective, however, if any of the beneficiaries is a minor or if there are unnamed beneficiaries ("Paul's children", for example, if Paul doesn't yet have children).
Contact the trust grantor and obtain his consent to the replacement of the trustee, if he is still alive. Some states require a living grantor to consent to the replacement of the trustee, and some states do not.
Appoint a replacement trustee and obtain his consent to the appointment. If the trust deed names an alternate trustee, appoint the alternate trustee. If the new trustee is an individual rather than a company, he must be at least 18 years old. To avoid a potential conflict of interest, don't appoint a beneficiary as trustee.
Draft a court motion to replace the trustee that includes legal grounds for replacement. These grounds may include mismanagement of trust assets, fraud, self-dealing or mental incompetence. Depending on state law, a court may grant an order to replace the trustee on the strength of the beneficiaries' consent alone. However, your motion may have a better chance of success if you include legal grounds for replacement. Have all beneficiaries sign the motion.