"Yes, Severus does seem the type, doesn't he? So useful to have him swooping around like an overgrown bat."
Going on alone from the potions room, Harry finds Professor Quirrell and the Mirror of Erised in the next chamber. Harry is shocked to find that Quirrell (and not Snape) has been trying to kill him and get the Philosopher’s Stone. Quirrell tries to use the Mirror of Erised to find the Stone but the Mirror gives it Harry. Realizing that Harry has the Stone, Voldemort has Quirrell reveal him. Voldemort has Quirrell physically attack Harry, but Quirrell’s skin burns when it comes in contact with Harry’s. Quirrell is about to finish Harry off with the Killing Curse when Harry defends himself by placing his hands on Quirrell’s face. This strategy works, but the proximity to Voldemort makes Harry’s scar hurt so badly that he passes out – and nearly dies before Dumbledore arrives to help.
During Quirrell's monologuing, he calls Voldemort by his name, which most of his agents never do. Quirrell also compares Snape to a bat - this comparison appears elsewhere in the series, as well, and led many people to suspect Snape of being a vampire until Rowling quashed that theory.
Quirrell says that in the Mirror of Erised he sees himself presenting the Stone to Voldemort. So Quirrell wanted to find the Stone, but not use it. He wanted to give it to Voldemort. According to Dumbledore's explanation later in the Hospital Wing, "only one who wanted to find the Stone -- find it but not use it" could get the Stone out of the mirror. Unless Quirrell was lying, he should have gotten the Stone at that point. Or maybe since he and Voldemort were essentially the same person at that moment, he actually did want to use it.
Note that Voldemort tells Quirrell to "use the boy" just after Harry starts trying to think of ways to get himself in front of the mirror; it's quite possible that Voldemort was using Legilimency on Harry at this point. This is the first of several occasions in which Voldemort approaches a problem by trying to use Harry to solve it. Three years from now, he will arrange to use Harry's blood to give him back the use of a body of his own, and the following year he will manipulate Harry into retrieving the prophecy orb from the Department of Mysteries.
It seems even more likely that Voldemort is using Legilimency at the point when he says that Harry is lying about what he sees in the Mirror, because Harry hasn't had much chance to betray himself through body language, even if Voldemort's eyes weren't covered by the turban.
Legilimency is almost certainly indicated when Voldemort suggests Harry take the Stone out of his pocket. Harry only had a chance to walk a few paces after acquiring the Stone before finding himself unable to move; without seeing into Harry's mind, it's hard to say how Voldemort could've guessed that the Stone had wound up in Harry's pocket.