"Training on" or "Training about"?
Solution 1:
"Training" and prepositions.
https://en.oxforddictionaries.com/definition/train starting from here, and http://www.oxfordlearnersdictionaries.com/definition/english/train_2 here:
to train for - To archive something. "To train for your first ride", "To train for promotion"
to train to - In order to do; to able to do. "They trained them to run very fast"
to train to be - To be able to be. "He trained to be stronger"
to train in - To be better in something. "She trained in pediatrics", "I don't have any training in interior decorating"
to train as - To be taught through sustained practice and instruction. "He trained as a plumber" (http://sentence.yourdictionary.com/training)
to train on - To educate someone in the use of something. "We trained him on the high diving board" (http://idioms.thefreedictionary.com/train+on)
to train about - *Rare find. "Teaching doctors in training about management and leadership" (http://www.bmj.com/content/343/bmj.d5672), "Get training about how to use GIS" (http://www.in.gov/gis/2350.htm).
[transitive] Train something (around/along/up, etc.) to make a plant grow in a particular direction. "Roses had been trained around the door"
Solution 2:
I ran a quick series of Google searches for "training about Photoshop," "training for Photoshop," "training in Photoshop," "training on Photoshop," and "training with Photoshop." The results are meaningful only insofar as they provide a snapshot of the relative popularity of "training about," "training for," "training in," "training on," and "training with" this particular software program. But despite their limited relevance, the results are interesting.
In order, from most matches to fewest matches (with number of matches in parentheses), the results were as follows: "training in Photoshop" (128,000), "training with Photoshop" (107,000), "training for Photoshop" (71,900), "training on Photoshop" (15,400), "training about Photoshop" (2,700). Those results suggest that "training in," "training with," and "training for" a particular software program have solid support; "training on" a particular software program is somewhat less popular; and "training about" a particular software program is rather rare.
I also ran a series of other simple Google searches in which I replaced "Photoshop" successively with "software," "the iPad," and "hardware." In every case, "training about" lagged behind the other four options—usually by a very large margin.
At the computer magazines where I've worked, the wording I heard most frequently was "training in [name of software program or operating system]" and "training on [name of computer or other hardware device]." Nevertheless, I wouldn't say that using any of the first four options ("training for," "training in," "training on," and "training with") in connection with either a particular software program or a particular piece of hardware constitutes a serious mistake. But I would not use the phrase "training about" in connection with software or hardware.