Step 3: Find and Place ("add") Components
Components are added to a schematic from the ADD dialog, which you get to by clicking the ADD button over on the GUI menu.
One of the major challenges of using Eagle is finding the components you want in the "official" libraries.
These libraries are extensive, not particularly well named (and the components aren't so well named either),
and seem to date back to a time when there was a different philosophy about multiple packages for a particular device. Resistors and capacitors have so many packages defined that picking the right one is difficult. Transistors, despite formable leads, tend to only have a single package defined. Many experienced EAGLE users don't use the standard libraries at all, copying common components and packages into private libraries or creating them from scratch.
The search capability of the add dialog is pretty good; you just have to be less specific about what you search for if you expect to find it.
When working from a published schematic, I prefer to add all the components in the approximately correct locations before I start connecting anything.
Once you've finished the add dialog, the part will get attached to your mouse pointer, and you can put it down wherever you want on the drawing page by clicking the left mouse button. The right mouse button rotates the part 90 degrees. The middle button, or left and right simultaneously (maybe) "mirrors" the part drawing, which may also be useful.