Probably the easiest way to start is by using the Rapid editor. This assumes you know how to use the Rapid editor. You can save yourself a URL with a few custom parameters to open the editor.
Rotate, and Move. (A bug: you can't switch directly from R to M, you must 'esc' or click to escape the move or rotate mode before selecting the other mode) #818
If address node exists, Shift+click to select building and address, then Combine.
Using JOSM
Install MapWithAI plugin.
When downloading data, tick the 'download mapwithai' checkbox.
If you use continious download, I suggest turning it off. mapwithai loads frequently, and takes long, and is frustrating when trying to work with it. Download an area, map it, then download another area.
Tip: when a building outline doesn't match the building, use the improveway plugin to fix it. That is considerably faster than adding individual nodes and dragging them. Don't forget to use Q to square the building after editing the outline.
Tasking Manager
Simple Task Manager works well for organizing and tracking your work. It tracks only by area, not by mapped feature like Map Roulette.