All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First and foremost we congratulate you on embracing Islam and we ask Allaah to make us and you firm on His Right Path and perform deeds of righteousness until death.
As regards masturbation, it is forbidden in Ramadan and other times, but in Ramadan it is more serious. Therefore, you have to repent and know that Allaah's Mercy is vast and He forgives sins. Allaah Says (which means): {And verily, I am indeed Forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them, (till his death).}[20:82]. So you have to perform righteous deeds in the future and do good as much as possible, as good deeds wipe out the bad ones.
As regards fasting, masturbation invalidates it, hence you have to make up the three days you invalided your fasting, but you do not have to expiate for them according to the most preponderant opinion of scholars as there is no evidence which makes expiation obligatory in this case. We advise you to be keen on anything that makes you stay away from masturbation and other disobediences. You can for instance keep yourself busy in what is useful like seeking religious knowledge, performing good deeds, and keeping righteous company, and keeping in touch with Islamic foundations and centres. You have to avoid bad company and indecent places, and also avoid pictures or literature that incite one's desires, etc. Finally, we remind you about the advice of the Prophet who said: "O young people! Whoever among you can marry, should marry, because it helps him lower his gaze and guard his modesty (i.e. his private parts from committing illegal sexual intercourse, etc.), and whoever is not able to marry, should fast, as fasting diminishes his sexual desire." So you have to be keen on fasting in order to preserve your chastity until Allaah enables you to get married.
Allaah knows best.