For those who wish to recite the whole order of prayers for "Bircas HaChammah", you can search for one, find it in Rabbi David Bleich's "Bircas HaChammah", or, im Yirtzeh HaShem, I will be able to post and/or link to the Tefillos.
In the Artscroll book of "Bircas HaChammah", the order of the tefillos is as follows:
The following is a list of the tefillos included in the Artscroll
"Birchas HaChammah" by Rav David Bleich:
1. Beings with "ויהי נעם" - Tehillim: 90; 17
2. Section of "Pasach Eliyahu" from the "Tikkunei Zohar" (17a)
3. Section from The Torah - Bereishis: 1; 14 - 19
4. Yirmiyahu: 31; 34 - 39
5. Tehillim: 136; 1 - 9
6. A special "לשם יחוד" - varying opinions regarding whether it's
recommended to say it or not recommended. (See Artscroll "Birchas
HaChammah")
7. Tehillim: 84; 12
8. Tehillim: 72; 5
9. Tehillim: 75; 2
10. Malachi: 3; 20
11. Tehillim: 97; 6
12. Tehillim: 148; 1 - 6
13. The B'racha of "עושה מעשה בראשית"
14. The tefillah of "אנא בכח" (the tefillah that is also recited by
many before Shacharis and Mincha)
15. Tehillim - Chapter 67
16. Tehillim - Chapter 150 (recited by some congregations)
17. Tehillim - Chapter 8 (recited by some congregations)
18. Tehillim - Chapter 19
19. Tehillim - Chapter 121
20. Baraisa from maseches "B'rachos" (59b) the complete text in the
following section: "תנו רבנן: הרואה חמה...דתלת נגהי ארבע".
21. The section from "Perek Shirah" of the sun - beginning with "שמש
אומר" and quoting the sun's shirah - Chabakuk: 3; 11. Artscroll then
writes "ואומר" and includes the pasuk from Yeshayahu: 60; 1. I don't
think I've seen a "Perek Shirah" with the pasuk from Yeshayahu for the
sun, but maybe there's such a girsa, as it is included in Artscroll.
(I wonder if this pasuk is included in the Artscroll "Perek Shirah".)
22. The tefillah of "E-l Adon..."
23. The paragraph of "שמך ה א-להינו יתקדש... ועל מאורי אור שעשית,
יפארוך סלה"
24. Tehillim - Chapter 33 (recited by some congregations)
25. The entire עלינו tefillah.
26. Tehillim - Chapter 74 (recited by some congregations)
27. The paragraph of "אין כא-להינו" through "אתה הוא מושיענו" (recited
by some congregations)
28. The short tefillah of "רבי חנניא בן עקשיא אומר...יגדיל תורה
ויאדיר"
29. Kaddish D'Rabbanan
30. A special short "מודים" tefillah for Birchas HaChammah.
31. A special "ויהי רצון" for Birchas HaChammah.
32. "Adon Olam..." (recited by some congregations)