I've been working with homeless cats for a long time, and I recommend that
you live-trap the cat, get him to the vet for an exam (include combo-test
to rule out FeLV/FIV), vaccination, worming, spay/neuter, flea treatment
-- and don't forget to look for an id chip in case a current owner is
involved), then confine him inside (cage or in a room of his own).  If he
is someone's abandoned/lost pet, he will soon begin relating to you in a
friendlier way and will bond with you.  If he is an outright feral and
wants no part of you, he can still live out his days in your backyard with
regular feedings from you.

This may sound like a pretty aggressive way to make friends, but it is in
the best interest of the cat.  He will be vetted and safe while you make
his acquaintance with food and shelter and hands-on contact.  Work with
your vet on evaluating the cat's temperment; try to find someone who has
experience with feral cats and a reputation for humane handling.

Campus Cats has an article of socializing shy cats (Taming the Tiger), but
our website is not in good shape right now.  I could try to find that for
you if you are interested.  I can also give you lots more advice on
catching the cat and getting is safely to your vet if you are interested.

Sharon Talbert
Friends of Campus Cats
Seattle

Step I    Keep good food and water coming.  It will happen in time if
he/she feels safe.  Good luck.  MLB

Once upon a time - sometime in the mid seventies - I was living in a
mobile home park and there was a tiny feral calico cat in the
neighborhood.  I started making friends by putting out food, then
going back inside, then staying outside but at ever decreasing
distances.  Over a period on some months, she eventually let me touch
her, but not pet her, and then only when she was eating.  She also got
very pregnant during that time and eventually had her kittens under a
nearby trailer.

Things took a turn for the strange on 4 July of that year.  It had
been raining for a couple of days when she came to the front door and
meowed.  I was startled, but opened the door.  She came in and started
inspecting the place.  She found that there were already three cats
living there, that there was plenty of food and water (she even
stopped for a snack to test the food), and that there were litter
pans.  She also inspected for hiding places.  Then she wanted out.

A little while later, she showed up again, this time with a red tabby
kitten in her mouth.  I let her in and she put the kitten under the
couch.  Then another red tabby kitten, and a third under the couch.

After delivering the third kitten, she lay down on the door mat and
called them - they came and nursed.  She went out and was never seen
again.

Since red tabbies are males, I gave them boy names.

After a month or so, the kittens became tame enough to handle, and low
and behold, all three were females.  They grew up to be mostly outdoor
cats, but were quite friendly when they were inside.

(Note: after some research, I discovered that a calico queen and a red
tabby tom produce red tabby kittens regardless of their sex.)