Lawrence spends a lot more time describing what people are thinking and feeling than what they're doing, but a few key props give us insight into the characters.
Hilda is a modern woman. We know she's a modern woman, because she's really attached to her car (a "nimble two-seater" [16.116]), just like a guy having a midlife crisis. Hilda actually is having a midlife crisis at this point; her husband is divorcing her because she has too many opinions of her own.
Everything about Hilda is uptight. No matter how unconventional her upbringing, she's still absolutely a member of the upper class. She "shut[s] the door of the car and [sits] tight" when she sees Mellors (16.200), and then starts the car "with a businesslike motion" (16.382). You'd never see her running naked in the rain or doing anything less than efficiently and firmly. Even Clifford grudgingly admires her: "she would make a man a first-rate helpmate, if he were going in for politics […]. [S]he had none of Connie's silliness" (16.160). In other words, Hilda is a Jackie; Connie is a Marilyn. You'd never see Connie driving her own car.
The way Hilda is attached to her car, Clifford is attached to his chair—only more so. Lawrence seems to forget that Clifford doesn't have a choice in the matter, because he basically makes fun of Clifford for being paralyzed. P.C., our narrator is not.
When we first meet Clifford, we learn that "he had a bath-chair with a small motor attachment […] of which he was really so proud" (1.6), and later that pride turns into "a certain conceit of himself in his lameness," even though the narrator says that it was "cruel for Clifford, while the world bloomed, to have to be helped from chair to bath-chair" (13.2).
Setting aside the fact that the narrator is almost as big of a jerk as Clifford is, this chair is no good. Wheels and motors are the worst thing about the modern world, and we're supposed to pity Clifford for having to get around this way—and maybe even hate him a little. The chair, and the paralysis, is the outward sign that Clifford's mind and soul have been corrupted.
For more on Clifford's chair, see "Symbolism, Imagery, Allegory."
Mellors always seems to have something in his hand, from a basket of bread to a hammer. When Connie first finds the hut, she notices all the tools scattered about: "a carpenter's bench, then a big box, tools, new boards, nails; and many things hung from pegs: axe, hatchet, traps, things in sacks, his coat" (8.35). In the next paragraph, she watches him use a hammer to build a chicken coop, and then later on he uses a hammer to break the frame holding the photograph of his wife (14.74).
So, he's useful to have around the house. But these tools also tell us that he's a decent, honest man in a world of men who are not decent or honest. There's no one prop that he's associated with, like a chair; he can use a variety of things and take care of himself in all sorts of ways. This almost makes him different from the miners. We don't see any of them, but we get the idea that they're not nearly as handy as he is.
We got nothin'. Connie isn't described with anything except once with some plants. And this actually tells us a lot about her. She doesn't need man-made tools to give her personality; she just is.
Props give us clues into the characters' personalities, but really the characters often don't have much in the way of personalities at all. For Lawrence, the characters aren't real people so much as they're little textual representations of his philosophy.
About Clifford, for example, we learn that "he had been so much hurt that something inside him had perished, some of his feelings had gone" (1.8). Of Hilda and Connie, we learn that "They were at once cosmopolitan and provincial, with the cosmopolitan provincialism of art that goes with pure social ideals" (1.10). Of Michaelis, we learn that he had "a slightly tail-between-the-legs look even now" (3.11). These are all moments when the narrator tells us exactly what to think. And they're effective. But even more often, the narrator uses the characters to tell us how to feel, in something that we can call…
Take Michaelis. Sure, we get a few impartial hints into his makeup. But we get a lot more through the viewpoint of Connie and Clifford, and even "society." Society, for example, decided that "Michaelis was the last word in what was caddish and bounderish" (3.6). It's not the narrator who calls him caddish and bounderish—it's "smart society."
And later, when he shows up at Wragby, we learn more: "At sight of him something in Clifford's country soul recoiled. He wasn't exactly … not exactly, in fact, he wasn't at all, well, what his appearance intended to imply" (10.15). If Clifford could get a complete sentence out, we'd learn that he thought Michaelis was just a little—or a lot—déclassé. Again, it's not the narrator who says that.
Or take Clifford: we get our best look at him through Connie's eyes, when, for example, she sees him "coming out in his true colours: a little vulgar, a little common and uninspired" (10.375). Is Clifford really vulgar and uninspired, or is this just how Connie sees him? Lady Chatterley's Lover seems to suggest that the question is irrelevant. The way people see you is the way you are.