The bicep is a small muscle, I wouldnt go with more than 4 or 5 sets (heavy).
As far as I have seen it is usually only the experts who do curls safely, and efficiently. I believe its not an isolation exercise, so dont use a preacher bench, or that bullcrap where you have ur back and head on the wall. But then once again dont use your lower back. When you curl dont isolate your biceps, recruit your shoulders, and upper back ( NEVER your lower back). If you use your lower back, you wont be going to the gym in a while if you do it too hard.
Also, like some have said above, do back. such as cable rows, cable pull downs, and Pull ups. PULL UPS are the ultimate upper body workout in my own opinion. And dont forget your tris (its 3 muscles), this contributes to big arms as much as your bis, like said above.
FYI: Workout your LEGS. Your legs have more muscle than any other part of your body. Your Quads are your biggest muscle. Exercising your muscles stimulates protein assimilation, increases the release of Gh, and helps nitrogen retention. With your legs being the biggest muscle group, you should take working your legs out seriously. With your Bis being so small ( in comparison ) they do little of the above.