By being useful as money, with use cases that are difficult to implement with other currencies.
In order for any cryptocurrency to achieve widespread adoption, it has certain hurdles it needs to overcome:
Ease of use: It has to be as easy to use as a credit card. I can't emphasize this one enough... If it takes longer and is more difficult to use to perform a transaction than a credit card, it will not succeed and will never be adopted as currency. Despite its relatively higher value in U.S. dollars, Bitcoin fails this rest abysmally, and will never be currency. Take a moment to consider the fact that there are plenty of people who have never even figured credit cards out; how will they use a currency system that is exponentially more complicated?
Speed: I want to buy a cup of coffee. I need to be able to walk up to the counter, order my coffee, pay for my coffee, and have the transaction completed and confirmed before I leave to sit down. There can be no delay of days or even minutes: It absolutely, positively must pass the coffee test to be widely accepted as currency.
Fees: It cannot be fee-based in a way that is directly visible to the end-user. That $4.00 mocha? It absolutely must cost exactly $4.00 (plus any applicable tax) to buy it. If it cost even one penny extra versus whipping out that credit card, people will use credit cards, and it won't be accepted as currency.
Stability: Its price must be stable. No one will accept a situation where the same cup of coffee costs $4 on Wednesday, $3 on Thursday, and $5 on Friday. If its value versus the dollar constantly rises, people will only save it, hoping to get rich by selling it later, giving it a purely speculative value that could plunge at any time. Conversely, if its value constantly goes down, no one will switch to it in the first place, because they're better off with dollars. Any if its value is utterly unpredictable and wild, no one will want to touch it with a ten-foot pole. Only stability ensures that it will be broadly accepted as currency.
Unique capabilities: There must be something you can do with the cryptocurrency that you simply cannot do with dollars or credit cards. The previous points will get you to something that is as good as dollars, but "as good" isn't good enough. To get people to switch, it must offer something compelling and unique.