Hi Debbie, sounds like the previous owner only applied one coat of paint (and in a hurry too), personally I'd lightly sand the drips/uneven areas with a fine-medium sandpaper, then remove any dust with a "damp" sponge. Once you have it down to a decent condition that you think looks good, paint it use, let dry overnight, then apply a second coat of paint. Since you stated that you're new to this, here's a few pointers. Use a brush (3"-4" wide) to cut in the corners (i.e., wall-wall, wall-ceiling, wall-baseboard, etc.), then use your roller to tackle the main portion of the wall. When rolling the walls first apply the paint to an area in kind of a ziz-zag pattern (left to right) then smooth out. Opps almost forgot, don't forget to use a drop cloth and masking tape to avoid ruining any woodwork and flooring. Good luck, and have fun!