We have a garden and have two barrels where we collect rainwater. This is usually sufficient to water our plants and vegetables. This is unless the time without rain lasts longer then 8 days. I am really wondering if you can predict how much volume one need to allocate to fully provide water for gardening.
A formula you could use would be to calculate water needs would be to figure out the area you're watering, the depth of water per week you need to provide, then convert to gallons and figure out how many weeks of storage you want.
So for a 20x20 garden, you have 400 square feet. If you want to provide 1" of water per week, that's 20 x 20 x 1/12, which is about 33 cubic feet, or about 250 gallons per week.
So if you wanted to have 8 weeks' worth of water stored, you'd need 2000 gallons of storage.
To take a different approach, figure out how much water you use in a watering session. (E.g. if you use drip irrigation.) Then multiply that by how many waterings you do in the period of time you want to have available in storage.
For example, if your drip system uses 30 gallons per watering, and you water 3x/week, then you need 90 gallons per week, or 720 gallons of storage for an 8 week period.
Keep in mind that if you plan to use your rainwater collection system for domestic purposes (e.g. flushing toilets, etc) then you need to account for that in your storage needs.
Also, if you plan to use a pond to store water, consider that you'll lose some water to evaporation -- especially in the middle of a hot, dry drought in midsummer.
If you don't mulch around your plants then doing that would mean you'd need to water your plants about less often, so your water supply would last longer.
This experiment looked at how much less water was lost by mulched plants. The result was a reduction in evaporation of about 25% when the plants were mulched, but I'm sure it varies depending on all sorts of conditions such as mulch type and thickness, plant type, and soil type.