Choosing a camera memory card can be pretty easy. There are just a few stats you want to keep your eye on when choosing a memory card. The first is size, you'll want to look for what I call the memory card sweet spot.
Memory Card Sweet Spot
What I'm referring too here is where the cost per size is the greatest. The size of memory cards is constantly growing and while a 1 GB a decade ago was unthinkable, now anything under a 1 GB isn't even worth putting into your camera. Then you have the other side of the spectrum that is pushing into the great size possible. At the writing of this post it was 128 GB for a cost of $142. Unless you are using the camera to record HD VIDEO most of the time, I wouldn't recommend springing for this option, but looking for the best value between 1 and 64 GBs: the Memory Card Sweet spot. At the writing of this post I would say the sweet spot is either 16 or 32GB memory cards.
You'll want to check your manual to see what cards will work with your camera. Typically cameras use SD cards, but there are SDHC and SDXC cards. Make sure that your camera can use these formats of SD cards. You'd hate to buy a 128GB SDXC card only to find that your camera only allows cards up to 64 GBs
This is typically represented by a "Class" number. The higher the number the better the write speeds. Not all manufactures are perfectly honest about this rating. SanDisck seems to under rate their class ratings so you typically get more speed than what the card is rated to deliver while other no name brands don't even meet the threshold for the ratings. The faster a card writes, the more shots you can take in burst mode. The class is also important for HD video. You're camera may tout incredible video specs in terms of resolution & frames per second, but you'll need a card that will be able to write fast enough to keep up with all that data you'll be recording. Typically your manual will suggest a minimum class rating.
Beyond the Card
You're no longer limited to just the space on your camera. Eye-Fi offers a card that has space on the card, then also has Wi-Fi built in so that you can wirelessly sync your photos to both your laptop (without internet connection) and online (with internet connection). If you are around Wi-Fi it will even capture the location of your photographs.
Some other specifications you'll want to look at when buying a memory card for your digital camera are:
Price. I would typically put brand ahead of price as it reflects quality. But I've found a lot of cards can get get the job done, as long as it has the right speeds and capacity.