The standards required depend on your involvement in the project. If you are an owner, you can "have a tank built" without any standards at all, though that's not the way it's normally done. You can hire consulting engineers and tank manufacturers who can furnish all the paperwork. The following are some standards that may or may not be involved in any given project:
API-650, tank standard
API-2000, venting standard
NFPA-30, governs siting and spacing of tanks
ASCE 7, gives seismic and wind loading for the US.
ASME B&PV Code, Section IX- Weld qualification
Possibly various building codes or fire codes applicable to the project.
Code of Federal Regulations applicable to the project (available online)
Any state regulations applicable to the project
OSHA rules applicable to the project