Rembrandt tulips require sites where they won't complete with heavy vegetation and tree or shrub roots. Sites that have morning or late afternoon sun will provide plenty of sun for the tulips to grow and bloom in spring.
Rembrandt tulips need soil with nutrients and good drainage. Amend soil to a depth several inches below the bulb with sand and peat moss. For clay soils, amend the soil with two parts compost to one part clay. When soil temperatures are about 60 degrees Fahrenheit in October, plant the bulb at least twice as deep as the bulb's size, or according to package instructions. If you plant the bulbs too shallowly, the roots will not grow well and the flowers in spring will be smaller.
Add 5-10-20 water-soluble fertilizer to the soil in late winter when you see the first signs of growth. Water the bulbs thoroughly after adding the fertilizer to prevent the bulb roots from burning. Plants need at least 1 inch of water per week during spring when the plant is growing and blooming. During summer, fall and winter, bulbs don't need extra watering.
After tulips have flowered and died back, use pruning shears to snip off the dead foliage and spent flower at the ground. If you leave the spent flower or seedhead on the bulb, the forming seed capsules will deplete the bulb's energy. Every two to three years, you can dig up the bulb in summer and divide the bulbs to make more Rembrandt tulip plants.