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Prompted by this...

Thousands of international backpackers are flocking to the Peruvian
Amazon rainforest to drink ayahuasca tea, a plant mixture made by
shamans and taken as part of a spiritual ritual. Those who drink the
thick rich liquid often throw up, but then experience hours of
mind-altering visions and a sense of internal exploration.

Source: Global Travel Industry News

I am informed that there is a burgeoning tourist market in Peru and Brazil for consuming hallucinogenic drugs, namely Ayahuasca. This drug reportedly will mitigate the effects of post traumatic stress disorder and similar psychological problems.

This drug is legal in Peru and Brazil, and there are a number "operators" who "administer" the drug.

But in South America ayahuasca is an integral part of some tribal
societies. In 2008, Peru's government recognised ayahuasca's status,
stating that it was "one of the basic pillars of the identity of the
Amazon peoples".

Source: BBC News

However, there are dangers involved...

British student Henry Miller, 19, died in Colombia after apparently
consuming the traditional hallucinogenic drink ayahuasca, or yage.
Emma Thelwell, who took the drug herself, explains why it has become a
rite of passage for some backpackers.

This question is about selecting a "operator" (or 'shaman' to be precise). Are there licensing standards that govern who can supply and administer hallucinogens? Or how would one distinguish a legitimate operator from a bogus operator who might provide an impure product or otherwise rip you off?

Also, for planning purposes, after consuming the drug, how long before you regain coherence and can safely resume your travels?

Your best bet would likely be to go to Brazil and join a church ceremony. Ayahuasca is legal there for religious use, and there are several well-established churches that use it regularly with a track record of not killing their members, most notably Santo Daime and União do Vegetal.

Church ceremonies (and the effects of ayahuasca) can last up to 12 hours, and you'll likely want a good night's sleep afterwards.

Interestingly, both have branches in the US and Europe which have (at least in some countries) been granted the right to conduct ayahuasca ceremonies legally, so you may not even need to travel to Brazil to have a legal and authentic experience.

Obvious caveat: joining a church and professing to share their beliefs when you just want to try their drugs sacraments is morally, ethically and possibly even legally dubious.

Opposite to @jpatokal answer, I'd say that you can do it safely on Iquitos-Perú, where a lot of people often go to do this "ceremonies" and there are a lot of places that offers this service, for example this.

The price is around 100$ per person per day (It's a pack that goes from 2 days to 8 days, depending on where you go to do it). For further information about the ceremony and recommendation here

And about which how to find trusty sites to do this, I'd highly recommend you 2 options:

Search on internet sites with a good recommendations like this or just go to the city (Iquitos) and ask the locals, they usually know which sites are the best, since they live there, and I can vouch that the people there is usually kind and helpfull.