I started building the faucet base by Extruding a 6-sided polygon in the vertical direction (Don't cap the ends), then added Splits. I extruded another 6-sided polygon in the horizontal direction (Don't cap the ends), and added Splits for the spout. I deleted 2 quads in the base (leaving 6 open edges), then patched in the spout using Lofts (Straight / Exact option). Next I performed Lofts to cap off the top of the base and the end of the spout. Then I Joined everything and turned on Show Points. From there it's a process of adding Splits and manipulating points (Vertices) to obtain the shapes you want (Alignment & Rotate tools work well here). Final step is to perform SubD to make everything smooth.
