These characters can teach Scarlett new Physical Skills for use in Combat, or improve her Level of Mastery of existing Physical Skills, if she has the necessary Skill Points (earned through Experience) and prerequisite skills. Not all teach the same skills; Scarlett can only learn new Skills (or improve her Level of Mastery of existing Skills) from a Teacher who knows that skill. See their individual articles to see which Physical Skills they can teach.
To learn new Physical Skills or improve the Level of Mastery in an already-learned Skill, Scarlett should move close enough to the Trainer character so that the "Talk to ___" Contextual Action Prompts appears. Initiating a Conversation with a Teacher will provide additional Dialog Choices. The first time Scarlett speaks with any Teacher, the Teacher will first introduce themselves. (Not all Teachers will automatically train Scarlett in Physical Skills; some, such as Yngvar, will only provide training after he has moved to a specific location.) Eventually, one of Scarlett's possible Dialog Choices with a Trainer will be to "Learn Physical Skills". Selecting that reply will bring up the Physical Skills screen.
Physical Skills that Scarlett can learn or improve with the current Teacher will be highlighted with a pulsing glow on the Skill screen. (Physical Skills will only be so highlighted if Scarlett as the necessary prerequisites. E.g., won't be available until she has first learned at least one Level of Mastery in the Ancestral Horror spell.)
To learn an available Skill, select it from among those that Scarlett can be learn and press the action key/button to buy an item. A pop-up display will confirm the action, showing the details of the Skill at the Level of Mastery to be learned and its cost in Skill Points. (That cost appears to always be 10 for every Skill.) Learned Skills are displayed in color on Scarlett's Skills page and the costs deducted from her Skill Points total.
Several of the Physical Skill Teachers Scarlett meets early in the game, such as Brawler, Yngvar, and Rangar, will also be able to act as Sparring Partners. They will allow Scarlett to practice some basic Combat techniques, such as Dodging, Blocking, and Combinations, which is useful to new players just learning the basic controls.