We don't know.

There is an ongoing controversy over the way the hoplite actually used his equipment. On the one hand, the great majority of vase paintings depicting men in hoplite armour show them wielding their spears overarm. On the other hand, some don't, and an underarm thrust seems more natural and more powerful. Literary sources are little help because they don't describe spear use in any detail. Reenactment crews seem to disagree over which is the best way to use the spear based on their practical experience.

The most detailed study on this ever produced is Christopher Matthew's A Storm of Spears: Understanding the Greek Hoplite At War (2012). He believes that hoplites used an underarm thrust. His many practical tests seem to prove his point: spears used underarm have greater reach, a more powerful thrust, and can be wielded far longer without causing fatigue. But this will never amount to hard evidence about the ancient Greeks.

More interesting is his analysis of the vase paintings I just mentioned. Matthew points out that the great majority of images in which spears are used overarm show these spears being gripped in the middle of the shaft. In pictures where the underarm thrust is used, the spear is gripped 2/3rds of the way down the shaft. His argument is that these grips correspond with the proper use of javelins and thrusting spears, respectively. In other words, most depictions of hoplites using their spear overarm really just show them throwing javelins, as they did through most of the Archaic period. Anderson already pointed out ages ago (Military Theory and Practice in the Age of Xenophon (1970)) that the underarm thrust is the usual one depicted on Classical vases, in contrast with the overarm thrust on Archaic ones. Matthew's idea, then, is that the men shown thrusting underarm are using their thrusting spears properly.

Now, this argument isn't watertight; exceptions are easily found. But it's very important to recognise that vase paintings followed various artistic conventions that we don't always understand, and they can't be taken as a straightforward depiction of reality. Matthew also points out that spears of men standing are routinely depicted as being far longer than spears of men fighting. Even if we take all this uncertainty to speak against his argument, at the very least it also casts doubt on the old view that spears were used overarm because that's what we see on vases.

Matthew also discusses the quaint matter of repositioning the spear. If we assume the hoplite thrusted overarm, the question is how he moved his spear from a point-upward "at ease" position to a point-downward "action" position, which would require him to reverse his grip on the shaft. There have been a number of suggestions from earlier scholars, including shifting the spear to the left hand to reverse the grip of the right, stabbing it into the ground and picking it up again, or even tossing it in the air and catching it with the hand reversed. None of these methods are very practical and none are supported by any evidence at all. This sort of imaginative speculation argues strongly against the idea that hoplites normally thrust overarm.

I personally find Matthew's case appealing on sheer practical grounds, but I know it hasn't convinced other scholars in the field. In ancient history it's hard enough to argue with the evidence, let alone against the evidence. In addition, overarm thrusting seems to accomodate the old idea that hoplite combat was a shoving match, whereas underarm thrusting would require more freedom of movement and more space between men (on this point I disagree with Matthew, who claims underarm thrusting can be done in a compact formation). Many scholars are therefore reluctant to give up the notion of hoplites poking down over the rims of their shields as they shoved. It's even been suggested that hoplites charged into battle with their spear underarm and then switched so that they could battle it out at close quarters with overarm thrusts. This is pretty much a desperate throw to make our practical assumptions about spear use go together with the (apparent) evidence.