I've been using this reel for a little while and love it. I'd like to keep on lovin' it so I'd like to know what is the best way to care for it? Should I simply blow it out with compressed air and dab a little oil on the part that drives the line winder spooler mechanism? How often should the reel be opened and greased?

If it is new and you can handle it, you can remove the spool bearings, clean them and apply a tiny drop of quality reel oil.  If you are not comfortable with opening it , leave it alone.  It comes out of the box well lubricated by Shimano.  At the end of your fishing year send to a reel service like DVT on this site and he will do what is needed to last you another year.  Again, if you are unsure of how to get inside...leave it alone and it will be fine for a year.

I like to tear down and service my reels at the end of every fishing season(clean everything, lube the gears, flush and relube bearings). I usually lube the level wind every 5-6 uses.