Terminology first: Training Points are used to train your Companions. Practice Points allow you to train outside your Pirate Class. For example, if you were a Privateer and had at least one Practice Point (seen on your character sheet [shortcut - the letter 'c'] in the lower right corner), then you could train in one of the other Pirate Classes (Musketeer, Buccaneer, Swashbuckler, or Witchdoctor). As mentioned by One-Eyed Jack, you get your first Practice Point around level 8.
Practice Points are obtained by doing at least the main line quests (I do all the quests so I don't have this problem) and Prospector Zeke's Quests. There may also be other Quests that give Practice Points - I am not sure.
When you buy back (Reset) a Companion's Training Points, only that Companion is affected. If you are a member of Pirate 101 (I'm fairly sure about Monthly and definite about Yearly), it only costs Gold to do. Otherwise the cost is probably in Crowns and the higher your level is, the more the expense.
If you want to buy back Practice Points for your Pirate, talk to any Trainer and press the Reset Button in the lower right corner. It can be done but the cost is in Crowns.