If you are new to resistance exercise, I recommend not jumping directly to weights. There are a lot of things you can do using body weight. (and they are free). Start by sitting in a sturdy chair (preferably without arms), place your hands on the edges of the chair near the front, walk your feet out in front of you so that your weight is on your extended arms, slowly lower yourself in front of the chair (not too far at first), then extend your arms lifting your body upward. Depending on your strength, you may only get one or two done at first, but if you keep at it 3 to 4 times a week, your arms will begin to strengthen. This exercise is almost entirely on your triceps, but if you contract your abs while you do it you will get a good exercise for your core at the same time. If you cannot extend your arms even one time, just lower yourself to the floor, get back to the starting position and slowly lower yourself again. After a bit you should get to a point where you can straighten your arms. Another trick to take the load off your arms until you are ready is to not extend your feet too far in front.

Get the book "Weight Lifting for Dummies". It has some great workouts for the triceps(batwings). I got it at my Library, It is an awesome book not only for lifting but for nutrition and how to prevent injuries as well!