Usually I plant garlic in the fall and let it go through winter and into spring. But what about growing it in spring? What care is needed for growing it over the spring/summer, if it can be done? I live in zone 4 (−30°F/-34°C).
Because garlic is a root product, by planting it in the fall there is more time for the bulb to grow, you simply get a tastier, bigger bulb.
You most certainly can plant in the spring. If you plant in raised beds and add a bit of balanced fertilizer, you should have decent sized bulbs by fall. I never remember to plant garlic in the fall. My bad.
Shallots, I have to add, I plant in the spring and they get huge by fall. They are some cross between leek and garlic, I think. Look like a cross between and onion and garlic and they are wonderful as a substitute for onions and garlic. Mild yet distinctive flavor. I don't think they store as well as garlic.
I've done it both ways (also zone 4) and always get better production if it's in the ground over winter (even if gotten in very late in the fall, or even early in the winter). Part of the problem is that it's going to be ready just about the same time, (late July or early August) as it's (IIRC) more based on day-length than age, so it will have less time to grow.
I don't know about zone 4, but in my area (zone 6) garlic is planted usually in spring, specifically in March right after the soil dethaws and is ready for harvest in July. When planted in spring, garlic competes for resources with weeds, so constant weeding is required, at least until the garlic grows well established roots.
For the cloves to start forming, plants need to be watered on a regular basis because drought prevents their formation.