I ran into this recently and thought it would be good to post something here for people who are also learning Eagle. This is another one of those nice non-intuitive things on Eagle.
Polygons have two things that are required to work as you want.
1 - Name the polygon the same as the signal to which it should be attached. So you can right click on a signal and see the name of N$16. Then right click on the polygon and select Name and change to N$16. Now the polygon will flow into that signal.
2 - Once you have the polygon drawn, it will only be dotted outline until you use the RATSNEST command. You can type that in the command line or right click on the polygon and select Ratsnest.
It took me tons of searching to figure out these two things. Hopefully it will help someone.
Also, if you are etching your own boards, you can define a bunch of polygons (or large GND polygons) to "use up" copper and reduce the amount you need to etch away. This will make your etchant last longer and finish faster.