"Si è messo" is the near past (passato prossimo) of "mettersi" (or indossare), literally "to put on oneself" (reflexive); the non reflexive form "mettere" would be "ha messo", with no real difference in meaning if used intransitively. English only has "to put on" (or to wear), so it's "he put on" or "he has put on".
Far past (passato remoto) doesn't use auxiliaries, although trapassato does... Anyway, reflexive form of verbs always uses essere as auxiliary, and transitive form always uses "avere". I'll list a few examples with both mettere (transitive) and mettersi (reflexive):
- Present: Metto la giacca / Mi metto la giacca
- Near past: Ho messo la giacca / Mi sono messo la giacca
- Imperfect: Mettevo la giacca / Mi mettevo la giacca
- Pluperfect: Avevo messo la giacca / Mi ero messo la giacca
- Far past: Misi la giacca / Mi misi la giacca
I'll spare you the "trapassato remoto" (used to described something that happened before another action that happened in the far past); I mostly wanted to point out the difference in auxiliary between the two forms.