The number 1 or the word "один" takes singular forms of nouns:
В комнате был только один человек. (There was only one person-SINGULAR
in the room).
It is true for all numbers that end in "один" (the actual word you say, not the last digit, so it's different for 11 'одиннадцать'):
В июле 31 / тридцать один день. (July has 31 day-SINGULAR)
11 / одиннадцать does not end in "один", but rather in "-надцать". That's why a different rule applies to this number. It doesn't defy logic and takes plural noun forms.
Он спал 11 часов. (He slept for 11 hours-PLURAL+GENITIVE.)
The word "один" can be declined for gender and case (so it behaves similar to adjectives):
одна девочка (one-FEMININE+NOMINATIVE girl)
один мальчик (one-MASCULINE+NOMINATIVE boy)
одно слово (one-NEUTER+NOMINATIVE word)
Я знаю одну девочку (I know one-FEMININE+ACCUSATIVE girl+ACCUSATIVE)
Я знаю одного мальчика (I know one-MASCULINE+ACCUSATIVE boy+ACCUSATIVE)
Я знаю одно слово (I know one-NEUTER+ACCUSATIVE word+ACCUSATIVE)
and so on.