Once the irrevocable trust is created, the trustee opens an account at brokerage. It will be titled something like James Smith Irrev Trust FBO Sarah Smith, Charles Wrangler Trustee, and carry the trust TaxID number. The brokerage will undoubtedly want a copy of the trust document.
The brokerage account is then funded with $$'s or stock transfers. Charles can then trade stocks in that account, and of course any capital gains, income, and dividends need to be accounted for on the 1041 Income Tax form.
This is assuming as pointed out, that the trust document doesn't prohibit stock investments.