I know that if i go to the dentist he/she will clean the gap between my teeth, but can i do it by myself at home?

Yes but: That's not a very good or smart ideal unless you are a dentist or dental hygienist. They are trained to do that and you are not. There is an old expression, 'the doctor who treats himself has a fool for a patient'.

You can try..: But if the space has calculus (hardened bacterial deposits) you will never get it off. You need the correct instruments and training to do so. That being said, see your local dentist for a thorough exam and cleaning, and then you can maintain your oral health at home between professional visits.