Congratulations on your new orchid! From my perspective as a plant, I am a Phalaenopsis, or "moth orchid," the most common type given as a gift. I may seem delicate, but with an understanding of my basic needs, I can thrive and rebloom for years to come. Here is what I require from you.
First, find me the right spot. I do not enjoy the harsh, direct rays of the sun; they will scorch my leaves, leaving ugly brown patches. However, I am not a fan of deep shade either, as I need light to produce energy. Place me near an east-facing window where I can bask in the gentle morning sun. A south or west window is acceptable, but please set me back a few feet or use a sheer curtain to diffuse the intense afternoon light. You will know I am happy if my leaves are a healthy, olive green. Dark green leaves mean I need more light, while reddish-green leaves indicate I am getting too much.
This is the step where most well-intentioned caregivers go wrong. I do not like wet feet! My roots are covered in a spongy velamen coating designed to absorb water quickly and then breathe. Constantly soggy roots will rot and kill me. Please water me thoroughly only when my potting medium is completely dry and my roots appear silvery-white. To do this, take me to the sink and run lukewarm water through my pot for about 15-30 seconds, allowing all excess water to drain completely out the bottom. Never let me sit in a saucer of water. I typically need this only every 1-2 weeks.
You may have noticed I am not potted in soil. In my natural habitat, I grow on trees as an epiphyte. Therefore, I am potted in a special mix of chunky bark, sphagnum moss, and perlite. This mix provides excellent drainage and air circulation for my roots. Do not repot me while I am in bloom, as the stress may cause my flowers to drop prematurely. The clear plastic pot I likely came in is ideal because it allows my photosynthetic roots to access light and lets you monitor my root health.
I originate from humid tropical forests. The average home air can be quite dry for me, especially in winter. To make me comfortable, you can place my pot on a humidity tray (a shallow tray filled with pebbles and water) or occasionally mist my aerial roots. Avoid misting my flowers and crown (the center where leaves meet) as this can lead to rot. I enjoy the same temperatures you do, ideally between 65-80°F (18-27°C). A slight drop in temperature at night can actually help stimulate my next flower spike.
While I am blooming, I am using stored energy. To help me recharge and produce new flowers in the future, I need to be fed. Use a balanced, water-soluble fertilizer formulated specifically for orchids, and dilute it to half or quarter strength. Feed me "weekly, weakly," meaning a little bit of fertilizer with one of my regular waterings. Once my flowers fade, you can cut the flower spike back to just above a node, and with proper care, I will reward you with a new bloom in several months.