How do you know what size external hard drive to get?

If you are going to use it as a Time Machine backup, please get a drive that has at least 2X the capacity of what is currently stored on the computer. I would STRONGLY recommend a 2-4 TB OWC Mercury Elite Pro. Do not, repeat DO NOT use if for any other types of overflow storage other than as a dedicated backup drive. If you want to store additional information then get a 2nd External Hard Disk. If you are not familiar with Time Machine please carefully read:

Back up your Mac with Time Machine

The reason I recommended OWC is you should invest in a quality External Hard Disk. Buying the drives that come on sale every other week at Walmart (WD, Seagate, Toshiba) are their entry level drives and not very high quality. What kind of value do you put on your data??

If you want to use it for time machine, go for a bigger one then your internal harddrive. I have a 500GB SSD in my 2009 iMac, and I have a 2TB drive for Time Machine. That way, I am sure my backup is secure and that I can go back way in time if nessecary

You need to give us more information. What do you intend to use the External Hard Disk for?