As far as getting onions to form larger bulbs : in my experience, its all about timing and using the right variety of onion. There are 'long day' varieties of onions that require 15+ hours of sunlight a day to trigger bulb growth, and 'short day' varieties that will trigger bulb production at 12 hours or less, so your geographical location and summer daylight length is important when picking a variety.
Planting them early in the season gives you time to get healthy leaves developed before the longer days of summer arive, when the bulbs will begin forming. If you wait too long to plant them, the onion spends it time building leaves, or begins developing its bulb too soon, before it has adequate leaves, either way resulting in smaller bulbs.
In any event, you want rich, loose soil for bulb growth. A mulch helps conserve water, and adding a fertilizer is a must. Onions have pathetic root systems when compared to other plants, so having a rich soil ready beforehand is a big help. Weeding is essential - they won't do well with any competition around them. For bulb growth, the best fertilizers to use are those with a lower nitrogen content. I generally use cow manure instead of a chemical based fertilizer [since I have cattle on my property and their waste is just there for the taking, wasting away, so to speak] but if you do choose to use a NPK type fertilizer, use one that is on a 1-2-2 ratio [like a 5-10-10]. I've tried both, and I personally think the manure works better for onions.
When watering, the most important thing is consistency: they won't develop large bulbs with sporadic watering. The soil should stay at a relative 'same' level of dampness throughout the season for best results. I generally soak the onions heavy once every four or five days, less if its rainy, and I keep a mulch on the onion bed to slow down evaporation.