Answer: Johnson grass is tough as nails and hard to eradicate! A single plant can produce over 5,000 seeds that can lay dormant for up to 20 years. Ugh! Unless you're dealing with a small amount, I don't recommend trying to "pull it out" because the rhizomes usually break off easily and are left in the ground to spread. If you yard is heavily infested, digging them out is probably not a reasonable solution either. No good management solutions exist for this type of grass short of tilling everything up and starting over. Even that's a bad idea, because Johnson grass thrives where there has recently been a soil disturbance. So to that extent, I can only offer you a few suggestions.
The best advice I can give you is to keep established plants mowed down close to soil level. Repeated mowing (bi-weekly) will help starve the rhizomes of nutrients, eventually causing the plant to give up (we hope). Using a propane torch may also help, but be warned that some studies suggest this actually encourages re-growth when done in the spring. Late winter is a better time for torching. If you live outside city limits, heavy grazing (goats, geese or sheep) will also help reduce plant vigor as well as spot treatment using herbicides.
If some patches of the grass are in lower concentrations in some areas, digging or tilling is effective providing that you remove all of the rhizomes (don't just chop them up with a tiller or you will end up with a thousand more little starter rhizomes). Reseed immediately with the appropriate grass seed and keep all other Johnson grass mowed down to prevent it from spreading to the newly disturbed area by seed. You're probably going to have to employ a number of these strategies (and a few years of patience) in order to rid yourself of this invasive menace completely.
Q&A Library Searching Tips