The Lycaste orchid genus, similarly to its relative Anguloa, likes intermediate-to-bright light, intermediate-to-cool temperatures, and high humidity. The flowers look rather different, though; they are more-or-less triangular in shape because the sepals point outward while the petals point forward. These orchids are very fun to grow, and will thrive if you get their care right.
The indoor types of orchids, including cattleya and phalaenopsis orchids, produce flowers that last months at a time. When these houseplants start blooming, the flower show continues for a long window—from four to 16 weeks. Cymbidium orchids produce up to 35 flowers per blossom spike, and each spike lasts up to eight weeks. Phalaenopsis orchid flowers can linger from 80 to 120 days.  
Epidendrum orchids are among the oldest genera in the orchid taxonomy. Originally, this genus included all epiphytic orchids. As knowledge of the different types of orchids expanded, the classification became much more refined; for example, there are now some terrestrial species in the Epidendrum genus, and a great many other species have been moved to other genera. Still, over 1000 Epidendrum species exist. They are usually easy to grow, and most have tall canelike pseudobulbs that lean all over the place and frequently produce keikis. Fun orchids!
Phalaenopsis, the Moth Orchid, is one of the most commonly available and easiest to grow orchid genera. It is an especially good choice for beginners to orchid growing. They have large, showy flowers that come in a wide variety of colors. Most species have several flowers per stem, but some have more, and others have as few as one or two. There are a great many hybrid varieties on the market.
Asking me what types of orchids there are is like asking me what types of people there are. Well, there are tall and short people, smart people and not-so-smart people, introverts and extroverts, people with different skin colors, and people from different parts of the world. Likewise, you will find many different types of orchids—different colors, species and hybrids, miniature and standard-sized, all different genera from different parts of the world. So I will narrow the question a bit, and look at it in terms of the orchids you will likely to buy and grow.

Oncidium, perhaps more accurately the oncidium alliance, are a group of plants from South America that span a wide range of habitats. Inside the oncidium alliance there are a number of genera that hybridize freely to create what we call intergeneric oncidium hybrids. These can come in all sorts of shapes and sizes but are generally characterized by large quantities of small to medium flowers borne on a branched stem that generally forms a Christmas-tree shape. The most commonly identified Oncidium are the yellow “dancing lady” type.
The main characteristic of this type of orchid is its very pleasant aroma, which means you will likely smell it even before you see it. The pure white flowers release their scent at night, are frequent bloomers, and can bloom all year long in many places. They are a small but showy type of orchid, and their leaves are long, reed-like in shape, and light green in color. They are also easy to grow and are low-maintenance flowers.
The indoor types of orchids, including cattleya and phalaenopsis orchids, produce flowers that last months at a time. When these houseplants start blooming, the flower show continues for a long window—from four to 16 weeks. Cymbidium orchids produce up to 35 flowers per blossom spike, and each spike lasts up to eight weeks. Phalaenopsis orchid flowers can linger from 80 to 120 days.  

Check your water. For a long time, serious growers insisted that orchids could only be watered with rainwater. Nowadays, most people just use tap water, and this is fine. However, be aware that treated water may have higher salt content, and some water is high in calcium. If you see deposits forming on your plants, you should seek out a new water source.
It sounds like it is not getting enough light. Repotting once per year after blooms have dropped is a good thing. Use a high quality bark mix for orchids or high quality sphagnum moss. If the flower spike dried out you did exactly the right thing by removing it. So try more light without direct sun and be sure to water only if the mix is dry. No wet feet for most orchids. Good luck

Epidendrum orchids are among the oldest genera in the orchid taxonomy. Originally, this genus included all epiphytic orchids. As knowledge of the different types of orchids expanded, the classification became much more refined; for example, there are now some terrestrial species in the Epidendrum genus, and a great many other species have been moved to other genera. Still, over 1000 Epidendrum species exist. They are usually easy to grow, and most have tall canelike pseudobulbs that lean all over the place and frequently produce keikis. Fun orchids!
Always water early in the day so that your orchids dry out by nighttime. The proper frequency of watering will depend on the climatic conditions where you live. In general, water once a week during the winter and twice a week when the weather turns warm and dry. The size of your orchid container also helps determine how often you need to water, regardless of climate conditions. Typically, a 6-inch pot needs water every 7 days and a 4-inch pot needs water every 5 to 6 days.
The leaves of some orchids are considered ornamental. The leaves of the Macodes sanderiana, a semiterrestrial or rock-hugging ("lithophyte") orchid, show a sparkling silver and gold veining on a light green background. The cordate leaves of Psychopsis limminghei are light brownish-green with maroon-puce markings, created by flower pigments. The attractive mottle of the leaves of lady's slippers from tropical and subtropical Asia (Paphiopedilum), is caused by uneven distribution of chlorophyll. Also, Phalaenopsis schilleriana is a pastel pink orchid with leaves spotted dark green and light green. The jewel orchid (Ludisia discolor) is grown more for its colorful leaves than its white flowers.
Always water early in the day so that your orchids dry out by nighttime. The proper frequency of watering will depend on the climatic conditions where you live. In general, water once a week during the winter and twice a week when the weather turns warm and dry. The size of your orchid container also helps determine how often you need to water, regardless of climate conditions. Typically, a 6-inch pot needs water every 7 days and a 4-inch pot needs water every 5 to 6 days.
Pollinators are often visually attracted by the shape and colours of the labellum. However, some Bulbophyllum species attract male fruit flies (Bactrocera spp.) solely via a floral chemical which simultaneously acts as a floral reward (e.g. methyl eugenol, raspberry ketone, or zingerone) to perform pollination.[8] The flowers may produce attractive odours. Although absent in most species, nectar may be produced in a spur of the labellum (8 in the illustration above), or on the point of the sepals, or in the septa of the ovary, the most typical position amongst the Asparagales.
Cymbidium carry tall stems with many flowers that have a more typical orchid shape. They are easily identified by their grassy leaves, and they readily form large clumps. Most common are the cool-flowering types, which need to experience a cooler winter (nights in the 40s for some time in the fall) in order to initiate flowering. Once the flowers open, they can last for up to two months or more, especially in a cool environment. These are very showy and rewarding plants, and a plant in a six-inch pot can carry three stems with 15 or more flowers each, depending on the type. 
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