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What exactly do you have now? It's going to depend on how much you want to spend. If you have a MacBook Air, upgrading the SSD is expensive. You could get something like a SD card drive like one of these:
http://www.amazon.com/Transcend-Jet...RJIS/ref=sr_1_5?ie=UTF8&qid=1448708808&sr=8-5

It's not as fast as an SSD drive, but if you just need a bump in storage, it's a compromise between getting a bigger SSD and going with an external HD.
 
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It's a SSD, not a HDD. :) If your MacBook Air is 2013 or newer, then it really isn't possible to upgrade the SSD. Apple uses a proprietary device that is not available from third parties. Several companies have been promising replacement drives ever since 2013 but AFAIK they have never materialized. The only way I know to upgrade would be to buy a SSD that someone has actually removed from their Mac. But if your MacBook Air is a 2012 or older model, there are third party SSDs available.

If you just got the computer and are still within the window, you might consider returning it and getting one with a SSD that is large enough for your needs. Otherwise you will need to get a SD card or extenal drive as smirking suggested.
 
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