Mince the garlic as finely as possible. Then use the side of your knife blade to mash and grind it into a paste for a minute or so (optional, but it helps to create a smoother consistency).
In a medium bowl, whisk together the garlic with the mayonnaise, lemon juice, and salt.
Use immediately or refrigerate until serving. Store the leftover aioli in an airtight container in the refrigerator for up to 2 weeks.