Answer: Obviously, the longer he is able to leave them on, the better. The halacha gives us a hierarchy of junctures (some of them based upon Kabbalistic sources):
1) Leave them on through the recitation of ‘four Kaddish-im (Kaddish-es)’. For the standard Ashkenazic service, this means: a) the half-Kaddish before Borchu (Artscroll Siddur, p.82), b) the half-Kaddish after the Shemoneh Esrei (p. 138), c) the Full-Kaddish after ‘u’Va l’Tzion’ (p. 156) and d) the Mourner’s Kaddish after ‘Aleinu’ (p. 160). (If you cannot wait that long…)
2) Leave them on through the third Kaddish (i.e. Full). (If you still cannot wait that long…) 3) Leave them on through the major part of ‘u’Va l’Tzion’, particularly the ‘kedusha d’sidrah’ (see commentary on p. 153), removing them before the last paragraph beginning with the words ‘Yehi ratzon mil-fanecha….’ (“May it be Your Will, etc.”) (Note: The Mishnah Berura writes that it is improper to be taking off and wrapping up the tefillin while ‘amein, ye-hei sh’mei rabbah mevorach’ is being recited by the chazzan and congregation. He writes that it would be like trying to do that while he was making a bracha - which is improper as well.)
Question: When should the tefillin be removed on Rosh Chodesh? On Chol Hamoed?
Answer: On Rosh Chodesh, the tefillin are left on for Hallel and Torah reading and removed before Musaf. On Chol Hamoed (i.e. for those who wear tefillin then), they should be removed before Hallel. (Note: A discussion about wearing tefillin on Chol Hamoed in general will be forthcoming, iy”H.)
MBY 26:1-2 If one has only one ‘tefilah’ (‘shel yad’ or ‘shel rosh’)
Although the Torah commands that we put tefillin on both the arm and the head, and that we do them in one continuous act, as we have learned, that does not mean that if one puts on only one ‘tefilah’, he has not accomplished anything. In fact, putting on each ‘tefilah’ fulfills one distinct mitzvah. This is true whether one has only one, or is able to put on only one!
Question: Which bracha/os would one say (i.e. Ashkenazi) if he was donning only the ‘shel yad’? Only the ‘shel rosh’?
Answer: If it is the ‘shel yad’, he should say only the bracha which ends ‘l’hani-ach tefillin’. If it is the ‘shel rosh’, he should say both brachos - ‘l’hani-ach tefillin’ and ‘al mitzvas tefillin’. (See above for a more thorough discussion of the brachos of tefillin.)