The minhag is to put on Tefillin in the Synagogue after having said Birchot HaShachar and Birchot HaTorah but preferably before the Shema in Korbanot and at least before Parshat HaTamid. Kaf Hachaim 25,3-4
The minimum requirement is to have Tefillin on during Kriyat Shema and Shmoneh Esrei. Shulchan Aruch Orach Chaim 25,4
One should wait until at least the kedusha of uva litzion before removing one's Tefillin.Shulchan aruch Orach Chaim 25,13
But ideally wait till the mourner's kaddish that takes place after alenu leshabeach and Al ken to take off one's Tefillin when finished the Prayers (mishna Brura Orach Chaim 25,13 55 quoting Arizal).