Can you get from Zaragoza to Granada in one day?

Yes, the fastest train connection is 6 hours (and others longer). See www.renfe.com or the Deutsche Bahn link at Looking Up Train Schedules and Routes Online.

Thanks Laura. Can I buy a direct ticket from Zaragoza to Granada on Renfe or do I have to buy each leg separately? If the latter, do you know each destination or have a link to a site that would show this?

Is this a summer trip? If so, be aware that Zaragoza can be stifling then. The train station (Zaragoza Delicias) is quite some distance from the historic district. Perhaps a 30-minute walk, but there are buses. The area around, the station is nearly a food desert. There's a decent business-class hotel right at the station, but it is so non-busymin the summer that its restaurant is closed. There's room service in the evening but npot at lunch. I don't remember whether there were any breakfast options at the hotel. There are a couple of casual places within the station ifself if you are desperate.

"Can I buy a direct ticket from Zaragoza to Granada on Renfe or do I have to buy each leg separately?"

I've learned that the Renfe site does not always show all connections. So, start with the Bahn site Laura gave you. Here's a direct link to it: http://reiseauskunft.bahn.de/bin/query.exe/en. See which trains you want to take.

Then, go to the Renfe site. You'll need this tutorial: https://www.tripadvisor.com/Travel-g187514-c80518/Madrid:Spain:Buying.Renfe.Tickets.Online.html. You should also plan to use Paypal, as US credit cards almost never work (I wasted a lot of time trying to get mine to work, whereas Paypal went through right away).

If you can book the route you want all on one ticket, do so. If you can't, then buy the legs separately. That's what I had to do for Toledo to Madrid and Madrid to Barcelona; the Renfe site showed only two connections for the whole day, whereas in reality there were many.

In the end, I realized it took FIVE websites to book my Spanish train tickets (Renfe, Bahn, Paypal, Tripadvisor - and Rick Steves to tell me about the other four). But in the end, it worked fine.

On the current timetable.

AVE 3990
Dep 10:20 ZARAGOZA-DELICIAS (Spain)
Arr 14:02 ANTEQUERA-SANTA ANA (Spain)
TRN13065
Dep 14:40 ANTEQUERA-SANTA ANA (Spain)
Arr 16:10 GRANADA (Spain)

Thanks everyone! You all are awesome and have made me feel more at ease. We're newbies at this (upper 60's) but still game for an adventure!