With a traditional juicer: Hold the juicer in one hand to stabilze it. Use the other hand to twist the lime half around the spiral center.
With a citrus squeezer: Place lime half in the squeezer, cut-side down, facing the holes. (It looks wrong but it's how you get the most juice without splashing lime juice into your face.) Squeeze hard and rotate the lime if needed.
With a citrus reamer, fork or spoon: Hold lime half in one hand. Insert the reamer, fork or spoon into the flesh of the fruit and turn in quarter turns to release the juice.
With an electric juicer: Follow manufacturer instructions.
Strain out the pulp.
Store in a food-safe, airtight container such as a mason jar. Use within one week, though it's freshest within 2-3 days. You can also freeze it into an ice cube tray. Use the frozen juice within 3-4 months.
Notes
Tips & tricks:
Use room temperature citrus. Let it sit on the counter for at least an hour before juicing. If you forget, microwave it in short bursts of 5 seconds until it is no longer cold. It should not be too hot to handle.
Roll citrus around on the counter to release the juices from the flesh.
Sharpen your knives before cutting citrus or any round fruit.