The branch of New Mexico government that administers New Mexico's LLCs and Corporations is the New Mexico Secretary of State. A link to the website is here.
The first step in the process is determining if the chosen name of your entity is available. The link to do that is here.
The second step is to file the appropriate formation document with the state. If your choice is to set up a New Mexico corporation, the online form Articles of Incorporation is here. The instructions are here. The relevant state statute is here.
The third step is to create the secondary formation documents. The secondary formation documents, for a corporation its Bylaws, and for an LLC its Operating Agreement, do not need to be filed with the State but are very important. The state does not provide free forms for them, but there are a couple of sites where you can access the forms for free.
New Mexico Corporate Bylaws, a New Mexico Member-Managed LLC Operating Agreement and a New Mexico Manager-Managed LLC Operating Agreement can all be found at Law Depot. It offers a free 7 day trial so you can download what you need and cancel and not be worse for the wear. Their charges, if you fail to cancel, are $33 per month.
Another source for free sample LLC Operating agreements (they do not have Bylaws) is Public Legal, a service of the Internet Legal Research Group www.ilrg.com. You can cut and paste the documents for free or buy them with some other related documents for $10.
A form Operating Agreement for a New Mexico Member-Managed LLC can be found here.
A form Operating Agreement for a New Mexico Manager-Managed LLC can be found here.
Finally, if you are forming a corporation, you will need to approve initial resolutions to appoint directors and officers and to issue shares. If you are forming an LLC, while not required, you may want to issue unit certificates to represent membership interests and you may want to appoint officers. The Forms and Resources and Online Minutes tools in After Incorporation have templates to help you take these steps.
Now that you have filed your formation document with the state and created your secondary formation documents you are ready to use all of the resources at After Incorporation to keep your company organized and in compliance with ongoing legal requirements.