"to try" is the normal word without much suggestive power. It may be used of an attempt undertaken experimentally, tentatively, or of an attempt ending in failure. It is the preferable word when testing or experiment are stressed rather than a venturing upon s.th.
(noun: trial):
'Try this wine, this beer, our liver pills.'
"Every time I tried to speak I was interrupted."

"to attempt" is very closely synonymous with "try". In precise use it always implies an actual beginning of, or venturing upon, that which one hopes to accomplish or carry through. It is sometimes preferred in references to ventures of greater magnitude. (noun: attempt):
"He attempted (to commit) suicide."
"William the Conqueror attempted, though in vain, to learn the English tongue." (Green)

from: Klein/Friedrich, "Englische Synonymik" (Hueber, München)