Learn Russian: Мне было пятнадцать лет, когда я решил копить деньги. - I was fifteen years old when I decided to save money.

In Russian, age is expressed using the Dative case. Instead of saying "I was 15," you literally say "To me it was 15 years." So, the nominative Я (I) becomes the dative Мне (to me).

Since the speaker is male, why is the verb было in the neuter form instead of the masculine был?

In age expressions, the subject isn't the person, but the quantity of years. Because this is an impersonal construction expressing a quantity, the past tense verb always takes the default neuter form было, regardless of the gender of the person speaking.

Why do we use лет for "years" here instead of год?

The word for "year" changes depending on the number. For 1, you use год, and for 2-4, you use года. But for numbers 5 through 20, including пятнадцать (15), you must use the genitive plural form лет (which historically means "summers").

How do we know the speaker is male if the pronoun я doesn't show gender?

We can tell from the past tense verb решил (decided). Past tense verbs in Russian change their ending to match the gender of the subject. If the speaker were female, she would have added an "-а" and said я решила.