While spells he had learnt and began to learn from his memories of texts he had read and could now far more vividly remember came much easier, he still had to create his own charms and such through employing sheer willpower and intent.
One thing he had reasoned out related to Gamp's Fourth Law, transfigured food could not be consumed without great harm to the person who ate it. However, if you transfigured existing food into another food, then Gamp's Fourth Law didn't apply. Knowing it could possibly kill him, but also knowing he really had no choice if he was going to do more than survive on this planet, he first tried to transfigure water into pumpkin juice.
It worked. Further, it didn't kill him.
His next effort was to transfigure the lizard meat he'd freshly caught into a roast lamb, his favourite meat. It, too, worked; so long as he made the transfiguration only last long enough for him to get the food into his stomach. He'd already realised that, once it was past his taste buds, how it tasted no longer mattered.
Realising as an 'omnivore' he properly needed plant-based food as well as meat to stay healthy, he'd also found a few edible plants that didn't make him sick; though they did taste foul, even after cooking them. He'd watched what plants the lizard rats ate and believed those to have the least risk. These, too, he cast weak transfigurations upon to last only long enough to get into his stomach.
After leaving Dumbledore's office, Tonks flooed directly to the Leaky Cauldron, the pub that acted as a gateway between muggle London and Diagon Alley. From there she apparated to a small grove of trees to the side of a park she knew of not far from Harry's home in Little Whinging.
There, she met Remus Lupin, who immediately scanned her for tracking and listening charms and the like. Surprising them both, they found none. Then both apparated to the Ministry atrium in London before then taking a floo, the only method of access to the place other than using the front door, to 12 Grimmauld Place in Kings Cross.
As they stepped out of the floo, with Tonks leading, Sirius was waiting for them. "How'd it go?" he asked. "Good," Tonks replied. "I only felt Dumbledore once try a weak probing passive Legilimency scan. The moment it touched my shields he withdrew and didn't try again."
Sirius nodded and raised his wand. Before he cast, though, he asked, "Ready for me to remove the memory block?"
She nodded back and replied, "Please."
Sirius performed a couple of quick swishes and flicks and Tonks felt certain memories pop back into existence in her mind.
"They're back," she sighed in relief.
The memories that had been blocked were of her knowing Sirius had been to Gringotts Bank and made arrangements concerning Harry's affairs. He'd gone directly there after being released by the Ministry on being found 'Not Guilty' of the crimes he'd finally been actually charged with. He'd first gone and demanded to see the life-stone he knew was attached to Harry's soul. It was still gently glowing, but greatly diminished. When he'd asked why it was behaving that way, the goblin's only guess was that 'Heir Potter' was alive but a very great distance away.
Now knowing that Harry was alive, he took control of the Potter estates as Regent and made damned sure no one at Gringotts could inform anyone else, especially including Dumbledore, that Harry was still alive - that his life-stone still glowed. Then added that no one was to know that he had taken control of the estate as Regent, or any other confidential matters relating to the estate.
Next, he formally renamed the now missing Harry Potter as his personal heir apparent and Heir of Black.
Again next, he took back Bellatrix LeStrange née Black's dowry paid to House LeStrange, annulled her marriage, then kicked her out of House Black by magically 'disowning' her. He used the excuses she'd both failed to birth an Heir of House LeStrange, as required by contract, and supposedly 'killed' the rightful Heir of her primary House, Heir Black Harry Potter, to accomplish that.
During the recovery of the dowry, the goblins discovered a Horcrux, soul fragment, in the LeStrange vault and that the 'phylactery', container for it, was the fabled Hufflepuff Cup. The goblins destroyed the Horcrux without destroying the Cup and moved the Cup to the Black vaults as part of the recovery.
Then he brought his cousin, Andromeda Tonks née Black, back into the family as a recognised daughter of the House, recognised Edward 'Ted' Tonks as her husband and a son-through-marriage of House Black and recognised Nymphadora Nanette Tonks as both their daughter and a newly instated daughter of House Black. Then added Andromeda as the Heir of Black after Harry and Nymphadora as the Heir after Andromeda.
Next, he stipulated that Narcissa Malfoy née Black and Draco Malfoy, her son, were kicked from the line of succession for House Black and had caused to be sent official notice to both of that fact. He did not put it past Lucius Malfoy, once he managed to 'escape' from Azkaban - that is, buy his way out - to try and have him, Sirius, assassinated believing his son would immediately inherit the Black Lordship.
With the parchmentwork out of the way he moved to have both the Black and Potter accounts fully audited.
Other than the payments that went out as stipends to those members of the House of Black still alive at the times, that account had not been touched. However, he was immediately informed that 'wizard Dumbledore' had borrowed certain artefacts from the Potter vaults over a decade ago and hadn't returned them. They included the Potter pensieve and a small stack of priceless books.
Furious, Sirius had them immediately retrieved by the goblins employing their recovery magics.
'Let that old bastard wonder what happened to them,' he thought. 'I certainly won't be telling him.'
One of the items they recovered through the magic was in no one's possession. It was a family signet ring with a chunky stone magically affixed to the underlying family crest - the House of Peverell crest. The goblins immediately detected it contained a Horcrux and had the Horcrux destroyed without destroying the ring, the phylactery, or the stone just as with the Cup. However, they informed him it had been recovered and that it had contained a Horcrux. The ring and stone were separated and went into the Peverell vault. The exercise, though, confirmed for Sirius that Harry was also the Heir of Peverell. A 'state' that had never before been confirmed by the Potters. The knowledge of that, too, was covered under the confidentiality contracts of Gringotts.
He also learned that Harry's trunk, still at Hogwarts at the time, had been 'rifled' through with a small sack of coin missing. However, he also found out that Ronald Weasley had 'claimed' Harry's Firebolt broom for himself, as he believed 'Harry would want him to have it'. However, he did not learn of those two until Dobby had turned up with a letter from Dumbledore and Sirius confirmed that Dobby had bonded to the boy.
The first thing he did after ordering Dobby to go and get Harry's things from Hogwarts - and finding out Ron Weasley had stolen Harry's broom and the coin pouch - was to send the elf with a note to Arthur Weasley, the boy's father, informing Arthur what his youngest son had done and that the Weasleys, as a whole, were now considered 'undeclared' enemies of House Black until he knew that the boy had been suitably punished.