To this day, Hoover Dam is considered a great architectural marvel.  Here are a few interesting facts:

First, how do you build a dam in the midst of a large, roaring river?  You dig diversion tunnels through the river walls and then plug up the river with boulders.  Wikipedia explains:

Tunneling began at the lower portals of the Nevada tunnels in May 1931. Shortly afterward, work began on two similar tunnels in the Arizona canyon wall. In March 1932, work began on lining the tunnels with concrete. First the base, or invert, was poured. Gantry cranes, running on rails through the entire length of each tunnel were used to place the concrete. The sidewalls were poured next. Movable sections of steel forms were used for the sidewalls. Finally, using pneumatic guns, the overheads were filled in. The concrete lining is 3 ft (1 m) thick, reducing the finished tunnel diameter to 50 ft (15 m).[46] The river was diverted into the two Arizona tunnels (the Nevada tunnels were kept in reserve for high water) on November 13, 1932. This was done by exploding a temporary cofferdam protecting the Arizona tunnels while at the same time dumping rubble into the river until its natural course was blocked.

After the river is dammed up, you have to remove the water and excavate down to bedrock.  "Cofferdams" were built upstream to help divert and block water from the construction site.  After the construction site was drained of water, excavation for the dam foundation could begin.  Again, Wikipedia:

For the dam to rest on solid rock, it was necessary to remove accumulated erosion soils and other loose materials in the riverbed until sound bedrock was reached. Work on the foundation excavations was completed in June 1933. During this excavation, approximately 1,500,000 cubic yards (1,150,000 m3) of material was removed. Since the dam was an arch-gravity type, the side-walls of the canyon would bear the force of the impounded lake. Therefore the side-walls were excavated too, to reach virgin rock as weathered rock might provide pathways for water seepage.

Lastly, here's an interesting bit of trivia.  Since falling rocks were the greatest work hazard during construction, many workers wore cloth hats that had been dipped in tar and dried.  These hardened hats successfully protected against skull injury.  Eventually, thousands of these "hard boiled hats" (later known as "hard hats") were put into use.

Read more about the building of Hoover Dam.