If my boyfriend been here in the US for 15 years, how can we get his green card?

In your situation, you cannot do anything for him unless you are married. After marriage you can file a Form I-130 petition for him. If he came to the US with a visa, you can concurrently file his Form I-485 green card application, even if his visa has expired. If he has no criminal record as you allege and if he came to the US legally with a visa, the whole process should be concluded in about 7 months,

Only through marriage or employment.

If your boyfriend was inspected when he entered the country and you are a US citizen, you can petition for him on form I-130 after you have been married and he can apply for adjustment of status concurrently on form I-485. If he did not enter the US legally, you can still petition for him on form I-130. However, he will need to apply for a provisional waiver on form I-601A after the I-130 petition has been approved, because he has been unlawfully present in the US in excess of 1 year. If the waiver application is approved, he can then apply for his immigrant visa and safely return to his home country for the visa interview at the US consulate.