Cut cardboard tubes into approximately 1 1/4- to 1 1/2-inch-long pieces. A toilet paper tube makes three pieces and a paper towel tube makes six pieces.
Stand the tubes on their ends in a flat-bottomed nursery tray side by side so they are touching and can support each other.
Fill each tube with seedling starting soil. Commercial mixes work or mix your own with one part peat and one part perlite.
Poke a hole with your finger in the soil in the center of each tube. Place a cucumber seed in each hole and then cover it. The hole should be about two to three times as deep as the diameter of the seed.
Pour about a quarter of an inch of water into the bottom of the tray. Monitor it closely as the cardboard and the soil soak up the water. Add more water, a little at a time as it gets soaked up, until the soil on the surface of the tubes is wet. Do not let any water stand in the bottom of the tray.
Place the tray in a warm and bright location to germinate. Do not place it in direct sun; this may overheat the seeds. Keep the soil moist but not wet. Water from the bottom and let the soil and seeds soak it up rather than watering from the top, which may disrupt seed growth. You should see signs of life in about 10 days.
Place seedlings that have produced two leaves in a covered, shady space outdoors protected from the elements for a week; move them to a partially sunny location for a week; and then transplant them to full sun in the garden. This process of "hardening off" a plant acclimates it to the garden environment. Remove the cardboard tube when transplanting or leave it on; in the latter case, the roots grow out of the bottom and the cardboard tubes decomposes into the soil.