For the most current and firsthand accounts about hyperhidrosis treatments and treatment combination results, it is best to check out the hyperhidrosis forum on this site. From my own experiences of having tried numerous treatments over the years, iontophoresis offers the best (albeit usually inconsistent) results of all nonsurgical treatments.
A typical order of experimenting with treatments is presented below. Alternative treatments such as meditation and breathing exercises (to possibly control your sympathetic nervous system) can be attempted too, although very few people manage to become experts at these skills due to the nature of the world and lifestyle we live in. It is interesting to note that most hyperhidrosis patients notice a cessation in sweating after drinking alcohol or right after waking up in the morning. And we do not sweat from our hands, feet, face or armpits when fully asleep. I imagine that expert meditaters in the Tibet or elsewhere can make their minds emulate a drunken "living in the present" or "asleep" state without actual alcohol consumption or without actually falling asleep and therefore list meditation as a possible treatment below.
I am a believer in some of these alternative treatments even though I have not tried most seriously and never ever seen a regular everyday person have success with any of them. Here is the most extraordinary example I have ever seen of the power of meditation in enabling control over the mind and pain and (sympathetic/autonomic?) nervous system.
Testing of monks who are able to drastically change their body temperature via Tummo meditation.
Here is an example of someone who is not a monk, but who is still able to use Tummo meditation skills to overcome extreme cold .
Some seemingly unusual things that temporarily relieve hyperhidrosis (based on my experiences) include hobbies that you are passionate about, swimming (especially in a salty ocean) and exercise/sports (after they are completed). When I am pursuing a hobby or interest that I really enjoy, sometimes I can get so engrossed in it, that after a while I realize that my feet (or for that matter, my whole body) emitted zero perspiration all the time during which I was engrossed in my hobby. For me, examples of such hobbies and/or interests include writing something interesting at work or in an e-mail, playing select video games, chess, reading something engrossing and so on. The younger you are and the more excited you are about various things and the more intensely you focus on your particular hobby, the better your likelihood of experiencing this phenomenon. In a way, this is basically the same concept as with meditation in terms of living completely in the present because your mind has been forced to focus on just one particular thing that you are passionate about.
Any time I swim or play a sport (or exert myself in other ways), I tend to have little to no sweat in the hours after I am done. In the case of sports, it could simply be due to the fact that my body has already exuded significant perspiration and is dehydrated, although I believe part of the explanation could also derive from my body just being relieved that the physical exertion is over, and being in a happy and satisfied endorphinated state.
I am not sure why I have zero sweat on my body after I have swum. It seems like this is especially true when I am relaxing on a beach after having swum in the salty sea. Perhaps the salty water blocks the sweat glands temporarily? Or it could just be a combination of being content and relaxed once the swim is over, and enjoying the peace of just lying down at a beach? The typical breeze at a beach also probably helps limit generalized as well as localized sweating.
Alcohol, marijuana and other drugs can also work at temporarily curing hyperhidrosis. This could indicate some kind of connection between the central nervous system and sympathetic nervous system as well as dehydration related sweat reduction in the case of alcohol. Unfortunately, the side effects from these "treatments" make them impractical in the long run (For the vast majority of people. I have met some lucky ones who have been alcoholics for decades, and remain healthy and thriving with no obvious mental retardation or cirrhosis symptoms).