There is no disadvantage on spells that require saves, only on attack rolls.
Since drow racial abilities synergize well with being a Charisma-based caster, Sunlight Sensitivity is not such a harsh penalty as it might seem initially.
You can get around the penalty by playing a caster with cantrips and spells that do not require an attack roll, but use a saving throw instead, and use those when under the penalty of sunlight.
As an example, a bard could use Vicious Mockery, a sorcerer Acid Splash or Poison Spray and a cleric Sacred Flame. Here is a list of spells with saving throws.
The Darkness spell (and 5th-level drow ability) mentioned in other answers might help too,too; but, is generally too harmful to your own party to be of frequent use, even as a Warlockwarlock with Devil's Sight.
Anything that grants advantage negates the disadvantage of Sunlight Sensitivity. "In such a situation, you have neither advantage nor disadvantage." (PHB, p. 173)
For example, as mentioned in a comment by @sadaqah, drow get Faerie Fire as a racial spell once per day at 3rd level and can use it to (potentially) negate the sunlight disadvantage.