Your character doesn't need to have any connection with the Underdark or with the other characters, prior to the start of the adventure. If you'd like your character to have a stronger Underdark connection, there are some additional background options in the sourcebook here that you can use.
Your character will start as a prisoner of the drow. When you make your character, roll 1d10 to see how many days your character has been held prisoner before the game starts. Your character may have scavenged some possession in their time there. Roll 1d20 and add the number of days that your character has been imprisoned, and I'll let you know what (if any) scavenged possession your character has found.