In short, Harry Potter learned early and well to never apply himself academically, a lesson which lasted right up until the day he met James Potter. It was like a dam cracking and then shattering, unleashing thoughts the boy had been burying since he was old enough to talk. The first night in his new room, he set himself to studying his new textbooks, starting with Potions. He was a remarkably good cook for an eleven-year-old (surprising the skills one picks up when the alternative is a frying pan flung at one's head), and he thought the principles should be similar. When he first came to a word he didn't understand ("What on Earth is a bezoar?"), he crept downstairs and claimed the Oxford English Dictionary which Aunt Marge had gifted to Dudley but which had never once been opened, and then he wrote the word and its meaning down in a spiral notebook leftover from the previous year of schooling. He started reading the book just after dinner and was surprised when he finally yawned, looked at his watch, and realized it was after midnight. He'd covered six chapters and filled three pages of his notebook. It was more homework than he'd done in his life.
Some people might have mistaken Harry's newfound studiousness for a desire to please the parents who had finally returned for him. Those people would be wrong. Harry had decided that he would excel in order to force his parents to acknowledge what a mistake they had made by tossing him aside, whatever it took. For ten years, the boy had been forced to accept his miserable lot in life as well as the vital need to keep his emotions in check at all costs. Nothing good ever came of getting angry at the way he'd been treated. But now, perhaps for the first time in his life, Harry Potter was angry. Absolutely and unreservedly angry. And it was an anger that burned cold.
For the entire month of August, Harry spent nearly every waking moment poring over the books he'd purchased at Flourish & Botts. He ate sparsely and always in his room, leaving the Dursleys to learn to their disappointment just how bad a cook Petunia was. Mornings were for magic, though just theory and history for now. It was apparently illegal for him to practice actual spells at home prior to the start of school, and while James implied with a wink that the Ministry turned a blind eye to minor spell-casting by pre-First Years, Harry was taking no chances. Afternoons were for etiquette and politics as he struggled to learn the nuances of the odd and insular culture he was about to join. Evenings were for whatever topics had left him with the most questions during the day, plus time spent practicing with a quill which was an entirely new but apparently vital skill to master. Finally, he spent from thirty minutes before bed practicing with his wand holster in front of a mirror, because the first time he'd tried to release the wand from its holster, he'd dropped it onto the floor, and if he did that in front of fellow students, it would be too embarrassing for words.
It was in the second week of studying wizarding politics that he finally came across the law which had actually required James Potter, under threat of jail time no less, to inform his firstborn son of his wizarding heritage and see to his education. After an owl exchange with the clerk at Flourish & Botts, Harry added Hutchinson's Commentary on Wizengamot Inheritance Law to his growing library. Luckily, his trunk had the best (and most expensive) expansion charms available on it. In a pinch, it even had a small room he could sleep in, although the idea of that reminded him too much of his cupboard for it to ever be comfortable.
On weekends, he would take a break by spending a few hours walking in a nearby park. Late on the second Sunday, he finally found what he was looking for: a small garden snake who, when addressed, hesitantly responded to Harry's voice in what sounded oddly like a Cockney accent. The snake, after expressing surprise at the sudden realization that it now had a name, introduced itself as ... Bob. And while Bob was not terribly knowledgeable about magic, he was somehow aware that Harry was "a Speaker," that Speakers were incredibly rare, and that no other snake known to Bob had ever met one. How Bob intuitively knew what other snakes he'd encountered remembered about a particular subject was a mystery even to Bob.
Even more strangely, Bob also indicated that he was only able to know these things while Harry talked with him or otherwise remained aware of him. Apparently, the moment a Parselmouth stopped regarding a particular snake as being worthy of attention, it went back to being a "normal" snake, though if the Speaker addressed it again later, it suddenly remembered everything that had happened in the meantime. But, if Harry actually assigned Bob some sort of task – like "watch over the park for a particular person" or even "go find other snakes and bring them here" – Bob could carry it out to completion, even following relatively complicated tasks in the process, only to revert to mundane "snakiness" when he was done. Strangest of all, the magic that powered Parseltongue seemed to be contagious. Bob could, if ordered to by Harry, go find other snakes and convey Harry's orders to them, which those snakes could then execute with at least as much intelligence and self-awareness as Bob himself had while under Harry's power.