Where are you supposed to start at when you come into shachrit during shema on a regular week day?
Prior to davening Krias Shema (its blessings) and the Shemoneh Esrei one needs to recite "Al netilas Yadayim", "Asher Yatzar" (since one is obligated to cleans one hands and system prior to prayer), "Birchas Ha Torah", and "Eloqai Neshama" (See MB. 52:9). Assuming these have all been said prior to arrival at Shul the Mechaber in the Shulchan Aruch (52:1) rules that if one will not be able to recite Shemoneh Esrei with the Tzibbur (congregation) then one may omit Pesukei D'Zimra and begin at the blessing for the Shema.
The Mishneh Berurah 52:1, however, cites the Sha'arei Teshuvah that one may omit [sections of] Pesukei D'Zimra provided that one is still able to recite Baruch SheOmar, Ashrei, and Yistabach [the essential components of Pesukei D'Zimra].
The Mishneh Berurah 52:7 says explicitly that if one will not be able to recite the Shemoneh Esrei with the Tzibbur by beggining at the first blessing of the Krias Shema then according to everyone one should pray Pesukei D'Zimra etc. in order rather than with the Tzibbur.
Excluding those prayers which cannot be made up (such as Baruch Sh'Omar and Yishtabach, which we have noted the MB says should be recited before anyways) one should recite that which was omitted following davening Shemoneh Esrei with the tzibbur.
One should say Netilas Yadayim, Asher Yatzar and Elokai Neshamah, (Skip the others and say them after tefillah) then say Birchos HaTorah if you have not said it yet. Say Baruch Sheamar, Ashrei, Yishtabach, Birchot krias Shema with Shema. All this skipping in order to make tefilla with the tzibbur by saying the amidah with the sheliach tzibbur (since he is too late to catch up with the tzibbur itself. Although the permission to skip is usually in order to pray with the silent amidah, the same reasoning applies to this case. (Psak from Rav Chaim Kanievsky). After Tefilla be sure to say the Berachos you skipped as well as korbanos. One may say the parts of pesukei di'zimrah he skipped if he desires.
For Sefardim: One should say all birchot haShahar first, no matter what. (Kaf HaChayim) The psak for sefaradim is like the Mechaber who says that one may skip Pisukei Dizimrah in order to make Tefillah BiTzibbur.
Tzibbur=Congregation Amidah=silent devotion
(Based on Shulchan Aruch, Mishnah Berurah, Kaf Hachayim, and oral tradition.)