In the 1860s in the US most roads were pretty crappy, not much more than dirt trails that had the trees cleared away. Most people didn’t have far to go and if it took longer in rainy weather, well you expected that.
As for “good roads,” according to this site, in heavily populated areas, some roads were paved. This could be cobblestone, blocks of wood, or in some areas (I’m thinking of near Milwaukee but I’m sure it was done elsewhere - on preview, California for instance) boards or planks. The cost meant that you didn’t do this all over, just in heavily traveled areas. Most city streets would still have been native dirt. Clay would have been preferred as it is hard when dry, but of course, very sticky when wet. Old photos on Minnesota towns, even into the early 1900s all have dirt streets.
In 1816 and British surveyor for Bristol revived the Roman road building techniques (with modifications) of using multiple layers to improve subsurface drainage and having a hard surface and side ditches to move surface water away. Some patches of Roman roads in Britain (and elsewhere I’m sure) can still be found and were used by foot and horse/oxen traffic for centuries after the Romans left.
Anyway, the Macadam technique was brought to the US in Maryland in 1823. Bituminous was not used as part of the construction technique until later in the 1800s.
Anyway, getting back to actually answering your question – In the 1860s the work would have been by manual labor and draft animals. I’ve seen pictures of horse drawn blades (like a motor grader) used to smooth out the working surface, carts to haul material and lots of guys with shovels. I don’t believe there would have been gravel crushers at the time and naturally graded materials would be used. (Some river or glacial deposits did make pretty good road building material in the natural state without crushing.)
City streets may have had drain inlets and underground piping of water to rivers, but this would have only been in the nicer areas of larger cities. Spots where the people were rich and important enough to get out of the muck and manure. Cobble stones and kerb stones would have been cut to size in quarries. I know some local (to Minnesota) quarries had steam power to haul rock and drill holes in the 1880s, but I don’t know if that was prevalent in the1860s elsewhere.
Of course, Wikipedia has an entry on the history of roads that might be interesting to you.
Steam shovels were not practical for road building until the early 1900s. They were big, bulky, expensive, and were best used for mining, canal building or other large projects. There is a lot that was done with human and horse labor.
You asked about rollers. Again, steam power would not have been applied to that yet. One technique of compacting the layers of road building material would have been to use hand tampers, a heavy flat plate with a vertical handle to lift it and let it drop. If they did use larger rollers they would have been pulled by horse or ox.