With the addition of an adjustable ab bench or other simple weight bench, you can get a full workout for both your core and extremities by following the guidelines of either videos, books, or just a dumbbell exercise chart.
The Internet - Many sites will have downloadable and printable dumbbell workout charts that cater to all sorts of exercise demographics - from full-time stay-at-home parents to jetsetting business professionals.
If you find that your arms and wrists become sore, you may want to add some exercises which focus on your lower arm to help you build strength such as the rotational dumbbell arm curl or the concentration curl.
If you don't mind working from your computer screen, you can keep your computer open while you work out, and actually follow dumbbell exercise charts with videos explaining the correct form for each exercise.
Strength training for weight loss is more than just picking up a dumbbell, but by choosing the proper exercises and doing them conscientiously, it is possible to reap the benefits of a stronger, lighter body.