I have a question:
Thanks for your question, Irene. If I have misunderstood your question, or if more introductory explanations of the liturgical events mentioned below would be helpful, please let me know.
If you are praying the weekday morning service without a minyan (quorum), certain prayers are skipped, and there is a slight procedural change concerning the Sh'ma. Here are the details:
Everything is the same as praying with a minyan until you reach the kaddish d'rabbanan (Scholar's Kaddish) at the end of the Preliminary Morning Service (i.e., shortly after "Ra-bi Yish-ma-eil O-meir..."). All instances of the kaddish, including this one, are skipped when praying without a minyan.
The Praise Section (P'sukei d'Zimrah) of the Shacharit (morning) service is normal, except that you omit the Mourner's Kaddish that some congregations say after Psalm 30, and omit the Half-Kaddish that closes this section (i.e., right after "Yish-ta-bach shim-cha la-ad mal-kei-nu...").
The Summons to Public Assembly (The Ba-r'chu) at the start of the Sh'ma Section is omitted. The two benedictions before the Sh'ma then proceed normally, but you insert one sentence just before the Sh'ma itself: "Eil Me-lech Ne-e-man". This means "God is a faithful King", and is an acrostic for "A-mein". It is intended to compensate for the fact that the Cantor will not be repeating the words "A-do-nai E-lo-hei-chem e-met" at the end of the Sh'ma. By inserting this, you keep the word count at 248, which is important for mystical reasons.
Everything proceeds normally right through the silent Amidah. But there is no repetition (so you won't have any k'dushah, nor a modim d'rabbanan, nor any birkat kohanim before Sim Shalom). Go directly from the silent Sim Shalom to Tachanun. During Tachanun, you skip the two pragraphs that begin at "Eil e-rech a-pa-yim a-tah..." and resume at either "Va-yo-mer Da-vid..." or "Ra-chum v'cha-nun..." depending on which custom your community follows. The Half-Kaddish that marks the end of the Amidah Section is omitted.
The entire (Monday and Thursday morning) Torah-Reading is omitted; you jump from the end of Tachanun directly to Ashrei.
The Full Kaddish that begins the Closing Section is omitted, and the ritual that usually follows for putting away the Torah (on Monday and Thursday mornings) is skipped. Everything else is the same except that all the kaddishes are left out. (e.g., the Mourner's Kaddish after the Psalm of the Day, the Scholar's Kaddish after any closing Talmud Torah that your siddur might have, the Mourner's Kaddish after Aleinu).
I hope this info is useful.