Copy training is where you learn to copy (write down) Morse code at a speed that is sufficient for use in radio communication.
Dahdidahdit is an actual Morse code tutor. You configure where you start (which letters you already know and what speed you can copy) and where you want to end (e.g. all Koch letters with a speed of 18 WPM and 18 effective WPM). Dahdidahdit then gets you to your desired target proficiency. All you have to do is practice frequently and be honest during grading.
The training is following a flow like this: first, one new letter (initially two: k and m) are presented for the reader to listen to. Then, there is a small game where random letters are played and you have to recognize the one that you just learned. When you think you’ve got the hang of the new letter, you proceed to the usual session where a whole string of letters are played and you have to write them down.
One word on „write them down“: In my personal experience, writing them down is a huge margin better than typing them into your computer. I lost two months of learning Morse code by typing the characters right into LCWO, thinking „I can touch type, this is nicer“. Imagine my face when I first sat down at the radio and tried to copy code. I knew where the damn letters were on the keyboard. I just had a really hard time remembering which character is on that key. And that took me so long that meanwhile many, many characters were sent, all of which I missed. Then I re-learned the code, writing the characters down. To speed things up, I used a script that allows to write characters in one very short stroke. This allows me to copy Morse code with 20/20 WPM right onto paper without breaking a sweat. You should try it!
This is what learning a new letter looks like:

(1) is the new letter in uppercase and lowercase. (2) is a suggestion how to write the letter down on paper. If you don’t want these suggestions, you can turn them off in the settings. (3) is the play button – pushing it will play the letter once. You can – and should – press the button as often as you need to get a feeling for the rhythm of the letter.
When you’re done, tap „Next“ and proceed to the following screen:

This is a small game to ease you into recognizing the new letter. You will hear a letter out of those you already know and need to decide if it’s the new letter or some other letter. In this screen, (1) is the letter to find. If you hear this letter, tap the left button (2), else tap the right button (3). You can repeat this as often as you want. For some new letters this will be a short thing, for others (think „-“ vs. „=“ vs. „x“) you might want to practice longer.
When you are confident enough, proceed by tapping on „Next“ and get to the following session screen:

Unsurprisingly, the play button (2) will start the session and Dahdidahdit will send Morse code letters for the duration printed below (4). If you need to abort for some reason (kids asking question comes to mind), tap on the stop button (1). This will get you to the grading screen that you also get to when the session time is up. If you just need a moment, tap on the pause button (3) and you can resume the session later.
Grading looks and works like this:

The text area (1) shows the text that was actually sent. You go through your notes and count how many errors you made. There is no fixed rule set for what constitutes an error, but I suggest counting wrong letters, missed letters and letters not actually sent. When I do this, I cross erroneous letters with a big backslash so I can later better distinguish between an error and an actual slash. Then you count your errors and tap the corresponding button. E.g. if you made 7 errors, you’d tap the middle button labelled „6-10“ because 7 is between 6 and 10.
If you often enough make few mistakes, Dahdidahdit will progress your learning by e.g. teaching you the next letter or, when you know all letters you want to know, by increasing speed or other annoyances like QSB. In the default setting, this means you need to get past the initial ease-in phase where the timing is a bit slower after you learn a new character. Then, you have to have three sessions with an error rate of 10% or less and no session with the highest error rate in the past ten sessions to move towards the next learning step.
If you ever feel that you can’t really remember the letter of the current level – e.g. because you took a longer break from practicing – you can select „Re-learn last character“ from the Copy training menu. If you are absolutely lost, you can enter the settings of the Copy training and move back even a few letters.