Place the peat pellets in a shallow bowl or pan and pour water into it. The pellets will expand into plugs, filled with peat, so allow them to expand completely. You may need to add more water.
Push one cucumber seed into each plug, 1 inch deep. Cover them with soil.
Place the container holding the plugs on top of a heat mat set to 85 degrees Fahrenheit. Keep an eye on the plugs and add water to the container if they begin drying out. The seeds should sprout within 3 to 5 days.
Plant the cucumber sprouts outdoors when the temperature remains 70 degrees Fahrenheit or warmer. Add 2 inches of compost to the cucumber bed's soil before planting.
Dig holes one-half inch deeper than the plugs and twice the diameter. Set each plug into its own hole and fill it with soil. The rim of the plug should be buried under the surface of the soil.