Put freshly cut flowers in a glass vase. Vases made of other materials may release harmful substances that could be absorbed by the flowers, causing an early death. Make sure the vase is spacious enough; you should be able to move the flowers around without taking them out.
Fill the vase with fresh water, to an inch or two below the top of the vase. Keeping the water level high will promote longer-lasting flowers. When you change the water (after it starts to appear dirty or the water level goes down), set the flowers gently on a nearby paper towel and thoroughly clean the vase before refilling. Check the water every other day, as Alstroemeria are known to be thirsty flowers.
Remove the flowers from the vase every few days and neatly recut the stems. Cut about 3/4 of an inch off the end of the stem. The newly cut end should not feel slimy or extremely soft. Be gentle when placing the flowers back in the vase.
Add flower food to the water in the vase to promote even longer life. Instructions vary with different types of flower food, but most should be added every few days. Always remove any debris you may see floating in the water.
Put the vase in a well-lit area to ensure the flowers receive plenty of sunlight. If in front of a window, rotate the vase frequently to allow sunlight to hit all of the flowers.