When you mention a birch tree, most people tend to think of the white or silver birch. This tree with its white papery bark grows across the northern United States. It is a short-lived tree lasting only about 60 to 70 years. It tends to be quite prolific, especially after forest fires that burn out larger stands of timber. You can start the seeds that fall in the summer for growing the following spring.
Collect or purchase the birch tree seeds. They will usually fall in August and if you are watching for them, you will see them start to fall. The catkins or strobiles will become brown and if you pull them off the tree, you will see the mature seeds that shake out into your hand. They are tiny with gossamer wings ready to help them fly.
Place several seeds in a container, such as an 8 oz. plant pot, filled with humus or well-rotted compost. This dark soil is at the bottom of a healthy compost pile, but is also available in garden stores. Sprinkle a very thin layer of soil on top of the seeds and then sprinkle them lightly with water.
Place the container in a plastic bag to hold the moisture and place it somewhere where it can go through stratification--this is when the seeds receive the cold rest time they need to break out of hibernation. You can place them outside in a protected area, in a non-heated garage or even a refrigerator vegetable drawer. Keep them there for six months, simulating the cold season outside.
Move the container to a warm and sunny spot, such as a south-facing window, after the six months. Make sure the soil is moist but not wet. They should sprout within a few days and then grow rapidly. Make sure you remove the plastic after the seeds show a green sprout. If several seeds sprout in one container, thin them out to one sturdy sprout.
Plant the seedling outside in late April or early May when the danger of frost has passed for your area. If you are worried about animals eating the seedling, you can grow it in a container for the first year, just make sure you are giving it full sun.