Acquire a root cutting of the desired mint variety from a friend, neighbor or nursery.
Dig compost or other organic material in the bed for the mint. Fill a tub with this soil for container gardening. Mint likes a rich soil. The exact location of the bed or tub is not important, but a spot with partial shade is ideal.
Plant the root cutting with the stem at the same level above ground as it was previously. Use the dirt clinging to the cutting as a guide. Water the cutting so the soil is moist but not soaking wet.
Water the cutting as necessary to keep the soil fairly moist for the following week or couple of weeks. Afterward, the plant should be sufficiently established that it only needs extra water during exceptionally dry spells.
Pull up weed seedlings from around the cutting as necessary. Later, the mint plant should be growing vigorously enough to need minimal weeding.
Harvest mint once the plant has produced an abundance of leaves. One plant produces all the mint a household can use, no matter how many mint juleps, mint sauces and mint sweets you make. Harvest as freely as you like. You can even cut back an established mint plant almost completely and it will be fine.