1. Navigate to Setup > Users/Roles > Manages Roles.
2. Edit the Role that will be given access.
3. Under Permissions tab > Lists sub tab, adds Accounts Permissions with Full as the Level of Access.
4. Click Save.
In the above scenario, the role will be given Full Access to all accounts listed in the Chart of Accounts (Lists > Accounting > Accounts). The User with that role will also be able to use these accounts on any transaction that they can access.
The ability to give restrictions on certain accounts is not currently possible and has been logged under Enhancement 42177 - Provide the ability either to restrict permission to particular accounts or to restrict access on reconcile bank statement screen.