Different states do it differently. Many states handle it at the county level—how an incident is handled depends on the county in which you get lost. New Mexico has organized SAR to operate at the state level. Search and Rescue operates under the NM Department of Public Safety (DPS), just like the state police.
There are a few consequences of being organized at the state level. On an official SAR mission, the Incident Commander is in charge of all the volunteer responders and the authority having jurisdiction is DPS. The means that a regional agency cannot command volunteer SAR responders; the chain of command for the volunteers goes up through the Incident Command to DPS, not through a local law enforcement agency. If a regional agency also has responders in the field, they maintain ultimate independent command of their own officers. However the regional resources can elect to temporarily place themselves under the direction of the Incident Commander for the duration of the incident in order to produce the most effective combined force. Alternatively, a scheme known as “unified command” can be employed, which is a tangent that is outside our scope here.
There is one paid SAR position in the state: the Resource Officer (RO). The RO is a DPS employee and acts as the single point of contact, organizer, and executive “decider” for the nitty gritty details of keeping SAR running in New Mexico. The RO maintains a Resource Directory of SAR teams and other resources in the state, and acts as a liaison for state police resources that get involved in SAR operations (for example the state police helicopter, Able 7 – check if it’s flying now).
Aside from the RO, the vast majority of SAR in the state of NM is volunteer. Occasionally some non-volunteer resources are particularly well suited for participating in SAR, for example Rio Arriba Fire and Emergency Services have valuable rapid-response UTV resources, and the private medical helicopter company Classic Air is particularly generous in their participation on SAR missions. However most of the people involved are volunteers, organized into local SAR teams, each with their own rules and membership and callout procedures and training methods.
In NM we adhere to the Incident Command System, overseen by FEMA at the federal level to be both sufficiently generic and sufficiently comprehensive to manage a wide range of disasters. The idea is that this one system is adequate for managing forest fire response, floor disasters, hurricane recoveries, volcanic eruptions, plane crashes, etc. The universality of the system is considered a benefit: the notion is that responders from across the country who are well-versed with the ICS system could fly to, say, the gulf coast to help with hurricane recovery and hit the ground running, slotting right into a productive role. In order to function for such disparate events, ICS is pretty generic. NM state SAR implements a few special things not found in ICS in order to customize it to our needs (e.g. Area Commanders and ORDMs). And since ICS is supposed to work for every scale from short and miniscule to long and huge, the system is pretty involved, and contains extra roles and responsibilities that we don’t need to use for NM SAR. On balance, the ICS system is hugely successful and has worked really well for NM SAR since its implementation by the “NM SAR Plan” in 1996.
As an aside: anybody can use the FEMA website to take online ICS training courses. It’s not exactly riveting material; FEMA is a US government agency after all, and the training definitely reflects it. But it gives you a taste of how ICS works, and the first two courses (ICS 100 & 200) are prerequisites if you want to get the official NM SAR certification.
There’s a lot to ICS (it’s a deep rabbit hole) but for the purposes of NM SAR it can be distilled down to only a handful of common roles. The IMT is the Incident Management Team. Every mission has an Incident Commander (IC), who is in overall charge of the mission. If the mission is large enough (and the IC is lucky) there may be some “staff members”, notably Section Chiefs (SC). The two primary section chiefs for SAR are the Operations Section Chief (“Ops”) and the Planning Section Chief (“Plans”). In the rare case that there’s a third SC on a mission, it is likely a Logistics SC (“Logs”), and extremely rarely one might even have staff for the positions of Public Information Officer, Safety Officer, or Liaison Officer.
Some semantics: a Field Coordinator (FC) is a person qualified and authorized to be an Incident Commander. The FCs are a pool of people that can act as Incident Commander. There could be numerous FCs involved in a single mission, but only one of them is the IC.
Operations and Planning SCs can be likened to tactics and strategy, respectively. Ops “runs the teams”, staying in communication with them, keeping track of where they are, where they’ve been, where they’re going, and what they’re doing. Ops responsibility is to the SAR teams themselves, more so than the subject of the search. Plans’ job is to stay out of the fray, keep a healthy overall perspective, refrain from descending too deep into the operational details, and to continually develop and refine the overall strategy. This starts with the scenarios (SAR-speak for “hypotheses”) about what may have happened with the subject. From the scenarios, Plans develops Search Objectives and The Plan. Not just “a plan” but “The Plan”; if the capital letters were insufficient to make it stand apart, we can call it by the full title, the “Incident Action Plan” or IAP.
And if there’s no Ops or Plans SC, all that stuff like running the teams and making The Plan still has to be done, it just falls to the IC to do it all by themselves. Many, if not most, missions can be competently managed by the IC alone. Obviously at a certain size and duration the work that needs to be done outgrow the abilities of a single person. A central notion in the ICS paradigm is that additional staff can be slotted smoothly into position as a mission grows, expanding the IMT to accommodate the complexity of the search.
For the curious, it was the State SAR Act (1978) that made all of these decisions about How We Do It in New Mexico. That and additional official SAR documents are listed on the Official Documents page.