Executive orders are usually first published in the Daily (previously Weekly) Compilation of Presidential Documents, then in the Federal Register. The Daily/Weekly Compilation of Presidential Documents includes EOs, signing statements, proclamations, etc. Each year, the entirety of the Daily Compilation is then printed in the Compilation of Presidential Documents (which is organized by year). This yearly compilation is in the Code of Federal Regulations Title 3 Compilation when that title is revised in print, starting from 1936. This is important for citation purposes, so you can be confident you are looking at the correct language, and so that you understand how government documents are organized.
For a thorough yet succinct review of executive orders, see Cong. Research Serv., RS20846, Executive Orders: Issuance, Modification, and Revocation (Apr. 16, 2014).
There are many ways of finding and researching executive orders. You will come across references to them in secondary sources as you start your research. You can also search collections of EOs.
Because EOs are published in the Federal Register or the Code of Federal Regulations, you can search any of those collections to find EOs as you would search them for any other regulation. You can also search the Compilation of Presidential Documents from the U.S. Government Publishing Office, the official publisher of the U.S. government.
A useful tool in any collection of EOs is a disposition table. This table will help you determine if an EO has been amended, revoked, or suspended by a subsequent EO. Here is an example from the Federal Register website.
These collections focus primarily on presidential materials/EOs. These materials can also be found on official government websites and any website that has collections of the relevant government documents, including HeinOnline, Westlaw, and Lexis Advance.