Regardless of whether you planted garlic in the spring or last fall, by mid May your garlic will be ready for a little fertilizer. High nitrogen organic fertilizers are best. The most commonly used forms of fertilizer for garlic would be blood-meal or even a synthetic source of nitrogen is best.
Try and keep your garlic well weeded, and apply a mulch such as straw if needed. Garlic doesn't like competition so if you have a lot of weeds near the garlic, it won't do well if it has to compete for nutrients with the weeds.
Water garlic deeply, about 2 feet every 8-10 days. As mid June approaches, begin tapering off how much watering you're doing.
A common myth with growing garlic is that the bulbs might only be mature once the green tops have begun to die back. This isn't always the case. Check for maturity even before the greens have turned yellow and begun to die. Sometimes the bulb is ready to harvest before this happens.
The bulb will be ready for harvest when you cut it open and can see that it has well developed cloves and three or fewer outer skins.