How does Hardy establish themes in the opening of Tess of the d'Urbervilles that relate to the rest of the book?
Hardy introduces two thematic threads in Chapter 1, part of Phase the First: The Maiden. One of these threads is quite largely spun while the other is very subtly spun.
The first thread of a theme carried throughout the book is the connection of the Durbeyfield family in the insignificant village of Marlott to the ancient Norman Conquest family of d'Urberville. This family was once great Norman warriors with wealth, land power but they lost it all, along with other great families, as Hardy briefly explains in a couple of places throughput the novel. Now the only branch of the family remaining is the insignificant Derbeyfield family.
[Parson Tringham said]: "Don't you really know, Durbeyfield, that you are the lineal representative of the ancient and knightly family of the d'Urbervilles, who derive their descent from Sir Pagan d'Urberville, that renowned knight who came from Normandy with William the Conqueror, as appears by Battle Abbey Roll?"
This background is significant to the plot, as the premise of the plot lies in trying to raise the family's circumstances by sending Tess to ask for assistance form the family that has adopted the d'Urberville name. This background is also significant to Tess's character development because it puts her qualities and inner traits into perspective and qualifies her distinctive nature and mannerisms.
Additionally, Tess's characterization is critical to the exemplification of the theme embedded in the subtitle of the novel: A Pure Woman as "faithfully presented by Thomas Hardy." In other words, Tess's character development exemplifies the theme of corrupted and corrupting circumstances that do not corrupt the qualities of a pure woman. This of course was Hardy's social comment against male behavior and the double social standard toward male versus female corruption.
The second thread of a theme, which is so subtly spun, resides in the mention of the locations of some of the ancient d'Uberville mansions.
[Parson Tringham said]: "None; though you once had 'em in abundance, as I said, for you family consisted of numerous branches. In this county there was a seat of yours at Kingsbere, and another at Sherton, and another in Millpond, and another at Lullstead, and another at Wellbridge."
Some of these ruined manorial estates come up again later in the story--such as Kingsbere, the site of the d'Urberville family burial vault--and connect all Tess's activities back to the d'Urberville line, for better or worse. The theme that these tie to is the inevitable destruction of those who are noble (Tess is innocent, naive and gullible, but noble) by the unrestrained behavior by those who are ignoble (i.e., not noble). Another instance set at an old d'Urburville manor is where Tess and Angel Clare spend their ill-fated wedding night, which is at the ancient d'Urberville mansion at Wellbridge in Froom Valley:
reaching Wellbridge, ... stood the house wherein they had engaged lodgings [in] the Froom Valley; once portion of a fine manorial residence, and the property and seat of a d'Urberville,...