In written and standard semi-formal (and above) spoken English, one would use "try to":
Try to be a better person.
Try to get the fishhook out of my thumb, please.
Try to find a pharmacy when you need one.
But in spoken English, we (Americans, at least) usually substitute "try and" for all those cases.
"Try to" makes sense because the "to" begins the construction of an infinitive: "try to be", "try to do", "try to act" and so on. "Try and" on the other hand doesn't seem to make any sense.
I'm curious how the "try and" crept in, and when. It's really tough to Google small words like these, so I'm not finding anything on the Web. Is it a contraction of something like "Try hard, and ..."?
Note: I've seen this question and it is somewhat related but doesn't tell me what I want to know.
Observe how, even on this site, people tend to gravite toward the "try and" construction.
Turning it on its head
Note that you can't make a negative construction with "try and":
It's raining. Try not to get wet.
It's raining. Try not and get wet. [?]
Even adding do doesn't help. The following means something different from "try not to get wet."
It's raining. Don't try and get wet.
Even use of to instead of and there means something else:
It's raining. Don't try to get wet.
"Try not to get wet" means try to stay dry. "Don't try to get wet" means avoid actively seeking out a soaking, and implies that a soaking might in fact be what you are looking for.