Make an Underdark campaign
The problem is that we human always try to emulate the context we exist in. We follow convention, and we do so instinctively. So when we try to make a character that exists in a good-aligned context, this instinct spills onto our characters and so we will be very drawn to trying to adapt the character to its context.
So rather than telling a player "do not fit the square peg to the round hole", make all holes square instead:
Make a campaign that is completely played in Underdark, and thus populated by Underdark-appropriate characters
Alternatively have a Drow party stranded on the surface. That was the basis of the first D&D campaign I ever played in and we kept that running for about 10 years. It is great fun playing an evil party!
More evil characters
Give the Drow character some evil company. It is easier to withstand the pressure if you do not have to endure it alone.
Avoid the odd one out; enforce race-typical alignment
To return the original question: how can you accommodate a singular evil character in an otherwise good/neutral context, and make the player feel comfortable with that and not have them feel they need to make — for instance — a good-aligned Drow?
I would advice against that actually, because even though strife and inter-character conflict is a great plot and role-playing hook, it is very hard to maintain, and it can cause discomfort among the players to always have their characters at each others' throats. In another campaign we had my character end up in conflict with two others. And although the roleplaying and the side-authoring (we love to author vignettes / novellas that hook into our play sessions) benefited greatly from this, in the end we were all happy when the conflict resolved.
So unless you have an experienced player that is comfortable with being the odd one out, that can play it in a way that does not strain the group, or you have effective plots that are well served by having an opposed aligned character... I would advice against letting opposed characters join the party. This in turn means that you either have to accept Drizzt's-type characters, or simply bar Drow characters from being created by enforcing race-typical alignment.