So I'm way late to the party, but (1/2):

The trouble is that we have very few first-hand accounts by peasants or even commoners from Tudor times, so it's hard to be sure what they knew and what they didn't. What we do have, though, is the Paston family. And they show us one major way that news, rumours, and gossip spread across the country and between social classes: via letters.

The Pastons started out as a yeoman family in Norfolk, but Clement Paston (d. 1419) was farsighted enough that in the wake of the Black Death he built up a sizeable landholding and sent his son off to get educated. Over the next couple of centuries, they gradually became a fairly prominent family in English society. And they will forever have a special place in the hearts of not just historians, but also Plantagenet/Tudor geeks like me, because they not only wrote each other letters, they kept them. For centuries. Starting in the early 1400s.

Here I'm focusing on their mid-fifteenth-century letters, a few decades pre-Tudors, because by Tudor times the Pastons were close enough to the court that their letters wouldn't really give you the commoner perspective that you're looking for - they're writing about personal conversations with the king, for example. In the mid-fifteenth century, they're still at more of a distance from the court. That should still be near enough to Tudor times to give you a respectable answer: there wasn't a huge shift in population, urbanisation or technology over those few decades, so it's unlikely that patterns of news transfer changed immensely between, say, 1450 and 1490.

A lot of what's in the letters is household business and domestic stuff that gives us a window straight into the writers and their world. Here's Margaret Paston to her husband John, in 1441, asking him to bring her back a new girdle from London, because she's pregnant and her old ones don't fit. Across almost six centuries, her excitement about the pregnancy still rings clear and bright:

I hadde never more nede ther of than I have now, for I ham waxse so fetys that I may not be gyrte in no barre of no gyrdyl that I have but of one. Elisabet Peverel hath leye sek xv. or xvj. wekys of the seyetyka, but sche sent my modyr word be Kate, that sche xuld come hedyr wanne God sent tyme, thoow sche xuld be crod in a barwe. Jon of Damm was here, and my modyr dyskevwyrd me to hym, and he seyed, be hys trouth that he was not gladder of no thyng that he harde thys towlmonyth, than he was ther of. I may no lenger leve be my crafte, I am dysscevwyrd of alle men that se me.

(I've never needed one more than I do now, for I've got so fat that none of my girdles will go around me except one. Elisabeth Peverel [probably a midwife] has been laid up sick for fifteen or sixteen weeks with sciatica, but she sent my mother word by Kate that she'll come here when God sends the time, even if she has to be wheeled in a barrow. John of Damm was here, and my mother told him about me, and he said it's the best news he's heard all year. I can't find clever ways to hide it any more, it's obvious to anyone who sees me!)

And in February 1477 we have the first recorded use of the word 'Valentine' for a loved one, from Margery Brews to John Paston (the younger brother of the baby Margaret was carrying back in 1441): 'Unto my ryght welebelovyd Voluntyn, John Paston, Squyer, be this bill delyvered'. Margery finishes off her love letter with 'I besech yowe that this bill be not seyn of none erthely creatur safe only your selffe' ('Please don't let this letter be seen by any earthly creature except yourself'). She had no idea what kind of family she was marrying into.

But in with the personal stuff there's also plenty of political news, including news about the royal family. In 1454, King Henry VI was suffering from some form of mental illness, to the point that he was unaware of the birth of his son. Here's John Stodeley's newsletter from that January, a few months after the Prince's birth:

At the Princes comyng to Wyndesore, the Duc of Buk’ toke hym in his armes and presented hym to the Kyng in godely wise, besechyng the Kyng to blisse hym; and the Kyng yave no maner answere. Natheless the Duk abode stille with the Prince by the Kyng; and whan he coude no maner answere have, the Queene come in, and toke the Prince in hir armes and presented hym in like forme as the Duke had done, desiryng that he shuld blisse it; but alle their labour was in veyne, for they departed thens without any answere or countenaunce savyng only that ones he loked on the Prince and caste doune his eyene ayen, without any more.

(When the Prince came to Windsor, the Duke of Buckingham took him in his arms and presented him to the King politely, asking the King to bless him; and the King didn't respond at all. The Duke stayed with the Prince beside the King anyway; and when he couldn't get any kind of response, the Queen came in, and took the Prince in her arms and presented him the same way the Duke had, asking the King to bless him; but all their labour was in vain, for they departed from there without any answer or recognition except that once he looked at the Prince and then cast down his eyes again, without any more.)

When Henry recovered, a year later, Edmund Clere wrote to John Paston:

Blessed be God, the Kyng is wel amended, and hath ben syn Cristemesday... And on the Moneday after noon the Queen came to him, and brought my Lord Prynce with her. And then he askid what the Princes name was, and the Queen told him Edward; and than he hild up his hands and thankid God therof. And he seid he never knew til that tyme, nor wist not what was seid to him, nor wist not where he had be whils he hath be seke til now...And my Lord of Wynchestr and my Lord of Seint Jones were with him on the morow after Tweltheday, and he speke to hem as well as ever he did; and when thei come out thei wept for joye.

(Thank God, the King is much better, and has been since Christmas Day...And on the Monday afternoon the Queen came to him, and brought the Prince with her. And then he asked what the Prince's name was, and the Queen told him Edward; and then he held up his hands and thanked God. And he said he never knew till that time, nor knew what was said to him or where he was while he was sick, till now... And my Lord of Winchester and my Lord of Saint Jones were with him on the morning after Twelfth Day, and he spoke to them as well as ever he did; and when they came out they wept for joy.)