No, it doesn't hurt. They will numb you, which is a small, quick pinch. The stiller you hold; the better it will feel. After numbing you, they will drill out the decayed tooth structure. Not painful, just noisy. Then they put some bond, aka glue, and fill the hole with filling material, aka hard stuff. That is all. Small cavities are not big holes. They can be simple sticky spots in the enamel that are very hard to see. When enamel becomes sticky, this is a sign there is active decay. This is why the always use that picky thing to check teeth. Another possibility is you have a cavity between your teeth, which is only visible on x-rays. Floss!

Spon, dental hygienist.