The propagation is the simplest of all plants. You can propagate this plant any time of the year by just inserting stem-tip cuttings 5-8 cm long in compost or in a glass of water. If you put it in water, plant it after the root system has formed into soil-based compost.
You need to renew the plant at least every 3 to 4 years as it loose its base leaves and become less attractive. Considering its potential of growing and propagating this should not be a problem not even to someone that never grow a plant.
If you want a plant that grow fast even if you don’t give it too much attention then this is the perfect plant for you. Just take a stem-tip cutting from a friend that have one and take it home, put it in water and in couple of weeks you can pot it. You’ll never get rid of it, your Tradescantia will keep growing and growing.