Over the years, there have been dozens of Hornady presses, you haven't said which one.
All pressed have some form of lever and linkage on the bottom of the ram. The axil pins are either nut and bolt assemblies or pin with keys, rings or cotter pins. Take the linkage off, slide or drive the axil pins out. At this point there may or may not be one last retaining ring just below the shell holder area, that would keep the ram from falling on you foot!
I nor anybody I know, ever disassembled a single stage press for routine maintenance. The risk of damaging parts (or loosing Them), was too great for the reward!
Do not lubricate with oils or grease. I use dry lube (from Elmer's) or One Shot case lube from Hornady. A graphite spray lube that dries quick (like Dri-Lock) works fine also.
Yes, Dillon recommends 10W30, but Dillon expects you to tear it apart every 50,000 rounds or so, they are the exception!
I have had old presses that were stored in wet basements. They had light surface rust on the ram. I coated them with a very fine oil (3-in-1) and scrubbed with 000 of 0000 steel wool and rinsed with spray break cleaner, move the ram to the other end of the stroke and repeat, dry lube and you are done. (1" emery cloth or plumbers sand paper works better than steel wool, when polishing with fine oil!)
Ivan