Commonly, if you make a gift to a minor you will use the Uniform Transfer to Minors Act (UTMA). Accounts under the UTMA are easy to establish. You don't need an attorney, and all banks and stock brokers have standard forms to set up such accounts.
Here is an extra tip! If you use the UTMA, please name not just the custodian, but also name a successor custodian. A father recently came to us after his wife's death. Someone had made a gift to their children using the UTMA. Apparently at the time of the gift, no one had suggested a successor custodian. We then had to satisfy the requirements of the brokerage company to get a court appointment of a successor. We had to file a court proceeding for the appointment of the child's father. In most such situations it is so easy to avoid the expense of a court proceeding by adding the designation of a successor custodian.
This information is general in character and is not intended as legal advice. Application of the law may differ substantially in individual situations. Before taking any action as a result of this information, a professional advisor should be consulted.