im new to road cycling (am a mtb'er) so i got a road bike. Should i cycle in the drops or holding the top of the handlebars, the part with out the tape on near the top of the brake lever? what do you do?

Just ride

Seriously do whatever is comfortable. I mostly ride on the top of the handlebars or the brake hoods (top of the brake lever). For really fast riding, sprinting, or descents I will get in the drops.

I'm also a mtb'er, but I've started road biking too. Most of the time while cruising, ride in the hoods (on top behind brake levers). The drops are used for a more aerodynamic position, whenever needed (sprinting, headwind, etc...). Some people use the tops of the handlebars for climbing or another position to switch to during a long ride. That's the general low down.

All of the above. Every aspect of road riding has a different effect on where I place my hands on the bar

On top for hill climbing, in the drops for sprinting on flats, or descending.

It's also best to alternate hand positions around the bar to ward off fatigue. I move my hands around every few minutes if not sooner.

Here's how I use my bars, maybe it'll help you:

Tops of the bars: seated climbing, level cruising

Brake hoods: climbing out of the saddle, sometimes for seated climbing, descending, whenever I'm shifting or braking, sprinting

Drops: aerodynamic purposes (riding into a headwind or trying to maximize a coast)

I tend to switch positions every few minutes to avoid tiredness in my hands.

Hold the handlebars? Who holds the handlebars?