The only verbal tenses where the Italian language makes a difference between male and female forms are composite tenses ("tempi composti"), where the past participle is used after the auxiliary verb "essere". In the case of "svegliarsi", all simple tenses look the same, e.g. "io mi sveglio" can apply to a male or a female subject. In the "present perfect" ("passato prossimo"), however, you will say "io mi sono svegliato" if you are a man and "io mi sono svegliata" if you are a woman, "noi ci siamo svegliati" for a group including at least a man and "noi ci siamo svegliate" for a group of women only. On the contrary, if the auxiliary verb is "avere", nothing will change most of the time: "io ho mangiato" is used both for a male and female subject. Conjugation is one of the hardest parts of the Italian grammar. I will be happy to teach you more about Italian verbs and grammar if you like. I hope my explanation was clear to you.

You can bookmark this page: http://www.italian-verbs.com/italian-verbs/conjugation.php?verbo=svegliarsi Remember that the "si" part is reflexive, and the rest of the verb conjugates as a regular "-are" verb.