Wash the beans under cold water and trim them to jar-length.
Peel and crush or thinly slice the garlic for flavor.
Get your canning equipment ready. Heat the jars without boiling, wash the lids with soapy water, and set aside the bands.
In a big saucepan, mix vinegar, water, and salt. Bring it to a boil while stirring to dissolve the salt.
In hot jars, add a clove of crushed garlic and a dill sprig. Pack the beans in, cut side up, leaving a half-inch of space at the top.
Pour hot brine into each jar, leaving a half-inch of space. Remove air bubbles with a utensil and wipe the jar rims.
Put a lid and band on each jar, tightening it to fingertip tightness. Place jars in a boiling-water canner. Repeat for all jars.
Boil the water in the canner, making sure it covers the jars by at least an inch. Boil pint jars for 15 minutes (adjust for altitude). Turn off heat after processing.
Let jars cool in the canner for 5 minutes. Then, carefully remove them without tightening loose bands. Allow further cooling for 12-24 hours. Check lids for a proper seal (no flexing when pressed at the center).