Marty wrote:

Hello,

Behind the apartments I live in, I frequently see a small black cat
with no tags or collar roaming around. I have tried to approach it to
bring it to a shelter, but it is too scared to let me come close
enough.

If this is a feral cat, it will be considered "unadoptable" and will be
euthanized at your public shelter.

The best thing you can do to help this cat is rent or buy a humane trap,
catch the cat, have it spayed or neutered and vaccinated, return it to
its territory, then feed and monitor it daily.

Does anyone have any advice about how to catch this cat?

You must use a humane trap. Don't try to grab the cat. One or both of
you will undoubtedly be injured. If the cat bites you and you go to a
doctor, the doctor is required by law to report the incident. An animal
control officer will be contacted and the cat will be captured and
killed.

Even though I can't bring it into my home (because I have already adopted 2
cats, and my landlord won't allow anymore) I'd like to give it a
chance to have a home,

Your landlord doesn't have to know you have a cat in a cage in your
house. While the cat is recovering from reproductive surgery, you will
be able to assess the cat's temperment. If you feel it has the
potential to be socialized, you can try to rehabilitate it and find a
permanent home. Be extremely cautious about surrendering any cat to a
public shelter. The vast majority of healthy, tame cats are euthanized.
Skittish, unsocialized cats don't have a prayer.

and take it off of the streets to prevent it
from having/making more kitties if its not spayed/neutered.

You can prevent breeding without "taking it off the streets". That is
the raison d'etre of Trap/Neuter/Release projects.