There are books in the library which describe the location, depth and encountered water level for wells dug in municipal golf courses, city buildings and other public work projects. These will help indicate how deep you'll have to go to hit water if these are near your property.
I installed a well on my property and did such research. It was well (no pun intended) worth it because I was able to keep peice of mind before forking out $15K for the dig. If I had not hit water, I would have been out this much.
I hit water in the first 30 feet but the quality was very low. This type of "close to the surface" water is refered to as "mole" water - either because its what seeps into the ground from the hole moles leave or that it flows up and down in a shallow manner picking up ground contaminants along the way.
After going down 300 feet, and punching through the remains of 3 river beds, my 7 gallon per minute water is like Perirre and I use it for in house and irrigation. My water bill went to zero (it used to be thousands) but my electrical bill went up about $40 (oh well

). After only 4 years it has paid for itself. From this point on, its a money maker - a mint in fact. Even my neighbors want to "buy" water from me cause its cheaper than what the city provides ($30 per 1000 gallons above a specific "tere".
Ok all that being said, there are a couple of things I would consider if I were in your shoes given the research and experience I have had.
1) Yes a hand well can be dug. Harbor freight (I think) sells well digging setups what can take you down about 100 feet. Other setups may be sold elsewhere. Be sure that the city ordinance does not prohibit the such a well. Even if it is only 10 feet deep, some nasty neighbor to the lot is likely to report its existence and then there could possibly be a fine.
2) Who owns the lot? A big question. Any improvements/alterations may aggravate the owner.
3) Professional hydrologists can be hired who, for a modest fee (maybe $200) will tell you exactly how far down the water is given that he will probably have accurate maps of the sub-terrain and access to the drilling logs of local wells. If your friends and you spend an hour each per week hauling water and their time is conservatively valued at $15 dollars per hour, doing the math will indicate that this expense is very reasonable. Another VERY inexpensive way to find out how deep the water in the area is, is to talk with other people in the area who already have wells and find out what the static level is. Just don't indicate why you are asking. Otherwise they will think you are trying to steal their water for "some tomatoes" and soon they will not be able to flush their toilets.
4) If you do hit water at a reasonable depth (100 feet perhaps) A wind mill can be used to pump water into a holding bin. You would tap this for your garden. A local high-school machine shop class may take on its construction as a school project so long as the materials were donated. They are not hard to make - check out youtube.
5) Again, if you do hit water, have it tested for nitrides, arsenic, and bacteria. If you pump a lot of water to the surface and it contaminates the surface soil, you may be liable.
6) If you do hit water, clearly mark it as grey water and NOT POTABLE. The last thing you want is a bunch of thirsty school kids crossing the property on their way back from a ball game drinking that water. So I would not put a regular faucet on the output but rather fittings which make it hard for humans to drink from the source or area of application.
I realise that this explanation describes a more technical approach to drilling a well, but here in California, where water is considered white gold, and water wars have been known to break out, I had to consider all the angles. Where you live things might be different.
As a side note, in the process of searching for the right location for my well, I learned some interesting true facts:
1) Jack and Jill went UP the hill to get a pale of water. Its strange but true, often drilling a well higher up on a hill/mountain will yeild water more readily than doing so at the bottom or in a valley.
2) There is no scientific proof that water witches work. Do not fall into the situation where you pay a water witch to locate water. I can site extensive USGS records and reports debunking this "craft".