Here is how the tapered spindles on the Oliver 288 and the 287 come apart.
The drawbolt goes all the way through the removable spindle and threads into the mandrel securing the spindle to it. The counter clockwise spindle will have a right hand threaded spindle nut. They also have a right hand threaded spindle draw bolt as shown here;
The clockwise spindle on a 288 will have a left hand spindle nut and a left hand threaded drawbolt. Remove the drawbolt by locking the spindle with the spindle locking pin and turn the drawbolt with a wrench. Once the drawbolt is removed the spindle can be removed from the mandrel. Depending upon how long it has been this can be somewhat difficult. A wrench on the flats at the spindle base should give you enough torque to spin the spindle slightly so it will just pop loose. If it does not come, you can apply a little heat at the base and try again. Here is the spindle removed;
Oliver supplied a spindle removal tool that threads onto the spindle, it has a rod that goes through the spindle to ride on top of the madrel so when threaded onto the spindle it supplies upward pressure to the spindle. If the spindle is not on too tight it works well, if the spindle is tight it will, instead of popping off the spindle, strip the spindle threads. For this reason I would use these with great care. Here is a pick of the spindle tool;
When putting the spindles back on be sure everything is meticulously clean. Once the spindle is remounted check the runout with a dial indicator. If the runout is excessive you can loosen the spindle, turn it a few degrees, tighten and check again. Continue this process until you get the smallest runout. You can use magic marker to index the spindle and mandrel so you can get it back on in the same place each time it is removed. Newer Oliver shapers have fine index lines cut into the mandrel and the spindle to aid in lining them up.