Get the serial number from about this mac.
Go to the apple support page, click on the support tab.
On the lower right hand corner of the page, click on check my warranty and repair options.
Enter your serial number and country. Click continue.
Look at paragraph 2. Waranty information about your product.
It may already have applecare on it. If so, yea! Have the prior owner transfer it to you.
It may still be within the original one year period. (If the prior owner registered it, it will go off of that. If not, it will find the manufacture date from the serial number. Then go and buy frakkin applecare on it.
It may be outside of the original one year window. Then, unless the original owner can provide documentation of the original purchase, you're SOL.