Variants are a tricky thing for a lot of people, so I will break down the process of how they are distributed. You might know this already, but just in-case another ready isn’t sure!
Most variants are buyer incentives. If your store orders 25 issues of Comic X, they get one variant cover. A variant is a different version (or different cover entirely) of the comic you are buying. There are different buyer qualifications for different comics. For example, you might get a black and white version of the original cover if you buy 25 copies. You might get a sketch version of that cover if you buy 50. So on, and so forth.
Superman Unchained came out last week, for example, and there were a lot of different covers. My store ordered 100 copies, and so we got variants for 10 issues, 25, 50, 75, 100….etc.
Now, because a store has to spend a certain amount of money to get a variant, they will be more expensive than just the regular comic. My store sells our variants from between $6 to $50, depending on the popularity of the book and how much more we had to spend to get it. A one in 10 variant, for example, will be cheaper than a one in 100.
So back to your question! It’s as simple as asking, but try to ask as soon in advance as you can. A lot of store put their orders in a month before the book comes out, so it’s easy to miss a variant. They might be able to up their orders to qualify, but it’s different for each store.
And be prepared to pay extra! If they usually order 10 copies of comic x, but need 25 to get the variant you want, be prepared to foot the bill for those 15 issues they wouldn’t ordinary be able to sell. But honestly, all you have to do is ask :)
A word of warning: VARIANTS ARE LIKE CRACK OH GOD DON’T START COLLECTING THEM I SWEAR TO GOD I HAVE LIKE 38 AND I ONLY COLLECT THE ONES I REALLY WANTS PLEASE SEND HELP.