When the man known as Taskmaster was a child, he discovered he had photographic reflexes after watching a cowboy program on television. He found out that he could duplicate the rope tricks exactly. He used these powers for his own gain, including becoming the high school star quarterback by watching a single pro football game. After graduation he considered becoming a superhero, but decided being a super-villain was more lucrative.
Watching broadcasts of superhuman activity, he executed several successful grand larcenies but underestimated the dangers involved in such work.
He thus used his profits to start up academies where he trained aspiring super-villains, including Crossbones, to become professionals. He designed a costume and took the name Taskmaster. He remained undetected until the activities of one head of an academy caused the Avengers to become aware of these facilities. Taskmaster battled Captain America and Iron Man, and was forced to flee; as during his confrontation with Jocasta he was unable to predict her future movements because of her lack of body language.
Taskmaster has what he calls "photographic reflexes". After seeing someone perform an action once, he can perfectly copy the action. He has used this ability to copy the fighting styles and skills of many heroes and villains, mixing them up and turning them into his own style. The people he has copied styles/skills from include: Beast, Black Widow, Bullseye, Captain America, Cat, Daredevil, Deadpool, Elektra, Hawkeye, Hulk, Iron Fist, Mister X, Ms. Marvel, Porcupine, Photon ( Genis-Vell), Puma, Punisher, Quicksilver, Razorfist, Scarlet Witch, Silver Samurai, Spider-Man, Swordsman, Thing, Thor, Tigra, Toad, Vision, Wolverine and Zaran. (In crossovers he has learned the skills of Batman and Huntress but it is unknown if he retains them in the normal Marvel Universe.)
This is just a short list, but it is impressive. He can only mimic actions to the extent that his body will allow. For example, he can copy the way Spider-Man fights, but can't copy his super strength. He can copy the way Daredevil moves to avoid danger, but he can't copy his radar. He can copy the fighting style of Deadpool but can't copy his unpredictability and healing factor. Copying skills doesn't give him an understanding of what is needed to do them either. He could copy a famous pianist's performance, but wouldn't be able to read sheet music. In a flashback he demonstrated something like this: when he was a child, he almost drowned after perfectly duplicating a swimmer's dive, forgetting that he couldn't swim.
To add to his abilities when he can't find someone to watch, Taskmaster uses the television. He watches movies and TV to study super-humans, athletes, stunt-men, archers, soldiers, wrestlers, etc. In this way, he has gained a wide range of combat as well as acrobatic skills including aerial acrobatics, gymnastics, boxing, martial arts (all the ones presently used and some historical ones), wrestling, swordsmanship, marksmanship, archery, car-jacking, and sleight of hand. By watching a video in fast forward, Taskmaster picked up the ability to move in "double time", giving him super speed for short periods of time. He also learned how to catch bullets during his mini-series.
Another skill Taskmaster has that is unconnected to his photographic reflexes is his ability to mimic voices. With just a couple hours of practice, Taskmaster can fully mimic another persons voice and speech patterns, a tool he uses for impersonation and breaking voice-activated locks.
Taskmaster has a lot of gear that he usually carries on him. He stole a wrist-mounted device from SHIELD that would let him create simple shapes out of energy. He used it to mimic weapons that go with styles he's stolen: Captain America's shield, Spider-Man's Web Shooters, Daredevil's billy clubs, Wolverine's claws, etc. Before he had the device he just carried all the extra weapons on him. Currently he is back to doing that instead of using the device, but there is no explanation as to why. He also uses an advanced image-inducer that allows him to take on the physical appearance of whomever he wishes.