There are various ways to score a card and many different types of competitions in which scoring will differ.
The term scramble is normally associated with a particular game called Texas Scramble.
A Texas Scramble is normally made up of a four ball who play as a team. Each player will tee of and you will opt to play the best drive, (note, you must each take four drives each) otherwise teams with a low handicapper may take all of his/her drives!
Once you have elected to take the best drive you each take the next shot from where the best drive finished with the driver of that ball going first.
Presuming the next shot lands on the green, you would each have a putt from the best ball closest to the pin.
The best (lowest) scramble score would then be marked on the team score card.