Here are some free exercise resources to fight flabby arms. (You can avoid buying weights by using canned goods to start.)
The American Council on Exercise has workout suggestions for every body part, including arm workouts. Each exercise has detailed directions, pictures, and a graph that indicates how difficult it is. Nifty!
Web MD suggests four basic arm exercises (modify the last two if you don’t have a bench).
About.com has a slew of exercises if you have a home gym or membership.
And of course there is my favorite: a video workout from the guy in 80s spandex who created eight minute abs. (below)