One of the ways to create verisimilitude in your writing is to have your characters dressed in period-appropriate (and class-appropriate) clothing. What does this mean for the writer of steampunk?*
The fashions of the 19th Century are your playground.
There are numerous websites devoted to steampunk and Victorian-era fashion. Heck, even whole books talk about the subject. A basic perusal of the scholarship out there reveals numerous styles of outfit for most any occupation you can hope to envision. Whether your character's an aeronaut, engineer, scholar, shopkeeper, or card sharp, you can find it there.
There are a few common items across almost all these styles though. For men, the basic clothing was trousers, a button-down shirt, a vest or waistcoat, a tie or cravat, and a jacket. Women, on the other hand, wore perhaps the most exhaustive list of clothing I've ever seen: chemise, three petticoats, a shift, a corset (depending on where in the century you're writing), and then the dress itself. It's enough to make a writer's head spin -- especially if you attempt to describe the process.
All the above is fine and dandy for the people who could buy their clothing new. However, the poorer folk tended to get their clothing like so: the rich bought it new and wore it until they didn't want to anymore; the clothing then passed to their servants; the servants wore the clothing out further, and eventually sold it to a secondhand shop; the secondhand shop would then sell the clothing to people one more rung down the social ladder, who would then resell the clothing when they were done with it; the clothes went further down the ladder to the street urchins, who wore the clothing until it fell into rags. The urchins would then sell their ragged clothes to merchants who sold them to the paper mills (paper still had cloth content at that point).
For steampunk-specific accouterments, remember that brass and copper were key metals in the Victorian period. Any accenting on clothing in those metals would add a decent steampunk feel.
*I should really say "what does that mean for this writer of steampunk?" considering you all know how much research I do. I swear, it's like an addiction or something.