Want Ashton in your party? Here's what to do (and what to avoid). There ARE spoilers here, so proceed at your own risk!

The recruitment begins for Ashton, in essence, after you finish the events at Mars village. Go to the port town of Herlie, where you will see two men conversing on the bottom of the screen- talk to them to overhear about a situation in the Salva Drift with a two-headed dragon. Go to the Salva Drift to see what it's all about.
After making your way through the mines (into an area previously inaccessible to you), you will find an unknown swordsman battling the aforementioned dragon. After a sequence of events, your party will be blamed for the unfortunate occurance. Choose the top option that you are given and Ashton will join you.
(Note: At this point you "have" Ashton, and the rest of these events aren't necessary. However, it's nice to do and provides good training (and some extra storyline), so you might want to do it.)
To fix what your party is blamed for, you must then travel to Mars village again, to ask the advice of the Elder. After you hear his advice, make your way to the Mountain Palace, near the town of Clik. The guard won't let you pass, so return to Cross to get a letter from the King, then back to the Mountain Palace. Once you complete this dungeon and beat the boss, you'll get one of the two things needed to exorcise the dragons possessing Ashton. After all this, return to Cross (heal and such), and then head northwest to Lasguss Mountain. After a long climb and another boss, you'll get the other item you need. Events occur, and Ashton will "officially" join your party.