score:3
TL;DR: You need to present your M&M account number at the check-in or apply for retroactive credit for a flight online at miles-and-more.com under the menu point "Mileage request".
There is no real harm in registering at all the frequent flier programs where you are able to earn miles on. The airline has your data anyhow already once you take a flight, so there is no privacy issue (as long as you do not use the card/number otherwise), and you do not pay any fees. Many programs also apply to car rentals, hotel bookings etc, so you can earn miles in several places.
To get the miles on your card, normally all you need to do is to present your card/number at check-in and you will get the points. Once you have a certain minimum amount of points, you will get the physical card. If you do not have a card yet, or forgot it, you can simply give them the number or apply retroactively on-line. You can also take a photo of your card and store it on your smartphone so there is no issue in case you do not carry them with you.