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If you are a member of the United’s MileagePlus Premier loyalty program, you are eligible for at least one free checked bag. The members with Premier Silver status can get only 1 checked bag free. If you need three bags free, then you should have Premier Platinum or Premier 1K status.
Another way to get a free checked bag, is to get a United credit card. The MileagePlus Explorer card will allow you and your one companion to receive your first standard checked bag free. The MileagePlus Club will allow you to receive free first and second checked bags for you and your one companion. But this card comes with a high annual fee - $450.