The trick to blackworms is cold, oxygenated, flowing water and a gravel substrate. They reproduce a bit on the slow side. Frankly, I found the time, effort and equipment required to culture them in usable amounts at home is cost prohibitive over purchasing them. They will breed freely in the substrate, but harvesting them is a pain and yields are very low on a small scale.
Purchased worms can be kept for weeks, even months in the fridge. When you first get the culture, rinse them really well with cold bottled spring water, removing any dead or decaying worms. Occasionally you will find various leeches, planarians or bloodworms in the culture. You can remove these if you like, but it is not necessary.
Next, you will need two disposable Tupperware type containers (I use the Ziploc brand myself) and one lid. Take one of the containers and punch a bunch of small holes throughout the bottom and first bottom inch of the sides. Place this "holy" container inside the other one. Add your worms and one bottle of cold spring water. Snap the lid in place and keep this container in the back of the fridge, or the vegetable drawer. Try to keep enough water in the container to keep the worms covered.
At least once a week, preferably two times, do a complete water change with cold bottled spring water, removing any dead worms. If you like, once a week "feed" them with about 1/8th of a teaspoon of goldfish flakes, ground to a very fine powder.
This is the "hard" way of doing it.
The easy way is to buy the blackworm keeper from the California Blackworms link here in the forums. It really is worth the money.