While this question answers how Snape knew Harry and Hermione were in the Forest of Dean, how did he know exactly where to send his patronus so that Harry would see it and be led to the sword of Gryffindor? Wikipedia indicates the area is over 110 square kilometers in size, so it would not have been an insignificant task to locate one small tent.
Did Snape over come the protective spells that Hermione would have cast or did he use another method to locate Harry? Or did Hermione forget to cast the protective spells (perhaps because of Harry's state at the time), which would account for Harry and Ron finding their way back in this question?
Depending on how the Patronus charm works, Snape has at least one method of locating Harry. As we have seen in several instances, the Weasley wedding and Harry's return to Hogwarts, the Patronus Charm can be used to deliver messages. In this case, the spirit guardian flies off toward the intended recipient. Considering that Snape has shown the ability to fly, it would not be inconceivable for him to Apparate to the Forest of Dean (to avoid tails) and proceed to cast and follow his Patronus to wherever Harry is.
Snape was tipped off by Phineas Nigellus, who was moving between his portraits in Hermione's bag and Hogwarts. Phineas overheard Hermione talking about their location in the Forest of Dean because Hermione forgot to close her enchanted beaded bag. Phineas then reported the location information to Snape in the Headmaster's office.
And now Snape stood again in the Headmaster’s study as Phineas Nigellus came hurrying into his portrait.
‘Headmaster! They are camping in the Forest of Dean! The Mudblood –’
‘Do not use that word!’
‘– the Granger girl, then, mentioned the place as she opened her bag and I heard her!’
‘Good. Very good!’ cried the portrait of Dumbledore behind the Headmaster’s chair. ‘Now, Severus, the sword! Do not forget that it must be taken under conditions of need and valour – and he must not know that you give it! If Voldemort should read Harry’s mind and see you acting for him –’
‘I know,’ said Snape curtly.
Deathly Hallows -- page 553 -- Bloomsbury -- chapter 33, The Prince's Tale
Ron got there because of the deluminator. He was probably the only human wandering the forest in the freezing cold. Maybe Snape searched and found Ron. Ron never says he used any enchantments to hide himself while he was trying to find Harry & Hermione.
I always assumed a Patronus works like a text message. You don't need to know where the recipient is, only whom you are sending a message to. This would answer the question of how Snape found Harry's exact location - he didn't but the Patronus did.
Another example to support this: Mr. Weasley couldn't have known where Harry, Ron and Hermione escaped to after the wedding but they got his message about the family being safe anyway.
Harry had to walk quite a while after he decided to follow the doe to the spot where the sword was presented to him. This makes sense if you think he could have been anywhere in the vast forest of Dean as far as Snape knew. He had to lure Harry to the sword from wherever he was in the forest.
I belive Ron's appearance had nothing to do with Snape's actions. Ron later explains how he was looking for his friends with the help of the Deluminator but in the end he only found Harry because he left the location guarded by their protective charms after following the doe. Very lucky!
No offence but Snape's no Muggle, he's probably the third most powerful wizard in the book, he's already shown he can get inside Harry's head and we all know what the power of love can do in the magical world!!! Or it could just be magic! 😉
JKR is hardly known for intricate flawless plots; no fantasy novels are flawless. I would personally say it’s the power of Snape's life be for Lily, and the unknown force of a powerful patronus carrying a powerful sword that appears to those who need it that finds them 😊