How do I fix a leaking connector between my garden hose and faucet?
It's possible to get the hose screwed on by hand tightly enough that it won't leak if your grip is strong enough; I think the strength required is within the normal range for an adult (mine is relatively strong though, so your mileage may vary). But before you get a wrench, there's a couple of things you should check:


make sure the threads on the faucet and on the hose are clean; if they've been disconnected over the winter, they could have picked up some dirt or grit which is preventing you from getting a good seal. 
the hose is supposed to have a rubber washer to make the seal against the end of the faucet. If it's missing, perished, or not seated correctly, then you won't get a good seal. You can get packs of washers (more than you'll ever use, probably) cheaply at the big box stores.




Once you've got those taken care of, try it with the hose screwed on hand-tight. If you're still getting leaks, you can try using a wrench, but remember that tightening is good, over-tightening is bad because you start to deform the rubber washer, which reduces its effectiveness. Get the hose hand-tight, then use the wrench to go another quarter-turn or so. If it's still leaking, it may be time to get a new hose.