Common Name Amaranth, tassel flower, love-lies-bleeding
Genus  Amaranthus 
Species A. caudatus (hanging tassels) A. cruentus (upright)
Family Amaranthaceae
Life Cycle  Tender Annual 
Tray Size  125
Plug Care Keep well watered, do not allow to become rootbound. Plant soon after receiving. Do not tease apart plants if there are multiple in a cell - plant them as one and you will have smaller, more manageable flower heads. 
Netting / Staking Only necessary in windy areas, otherwise very sturdy.
Temperature Range Not frost tolerant - expect them to grow best during the warm days of summer. 
Spacing 12" if pinching - will tolerate much tighter spacing for smaller stems that are easier to work with. 
Soil Preference Fertile, well drained soil, neutral pH.
Day Length Facultative long-day plant. Longer days and warmer conditions cause the plants to grow faster - plant successions up to 4 weeks apart in the height of summer for staggered blooms, any closer together and they might flower at the same time. 
Pinching Optional. If spacing single plants 12" or more apart, pinch when the plant is about a foot tall to promote development of smaller side branches. Single plants at this spacing, if left un-pinched, will grow massive and may be hard to use in arrangements. Plant multiple plants closely together (sometimes plugs will come with  multiple plants in each cell) and they will stay small and useable. 
When to Plant In the spring, after all threat of frost has passed. Plant multiple successions two weeks apart from last frost through to mid summer for continuous blooms until frost. 
Harvesting For fresh use, harvest when approximately 3/4 of the flowers on the inflorescence are open. For drying, harvest slightly later when the seed has begun to set.  
Post Harvest Care Place cut stems immediately into cool water. Expect a vase life of up to two weeks if floral conditioners are used. 
Diseases / Insects Flea beetles will riddle the leaves with holes. Remove leaves after harvesting. 
Bailey's Notes Plants will benefit from a liquid fertilizer application while the plants are growing. Avoid too much nitrogen when the plant initiates buds or there will be lots of vegetation with few flowers. 
Resources

Cornell Amaranthus Guide

How to Grow Amaranthus