The gemara in Shabbat 118b is the basic starting point for understanding pesukei d’zimra. 

תלמוד בבלי שבת קי”ח ב

אמר רבי יוסי יהא חלקי מגומרי הלל בכל יום…כי קאמרינן בפסוקי דזמרא. 

Bavli, Shabbat 118b

Rebbe Yosi said, “May my portion be among those who complete Hallel every day”…When we make this statement, we are referring to pesukei d’zimra.

Rebbe Yosi’s statement here is aspirational, “יהא חלקי – may my portion be;” he expresses a desire to do something beyond the letter of the law. At this early stage, the practice of pesukei d’zimra was clearly optional. Only with the formalization of the sections to be recited¹ as well as berachot does pesukei d’zimra become an obligatory section of Tefila.

The gemara here presents us with two ideas of Hallel. One is the tefila recited at appointed festive occasions (מועדים); the other is a daily opportunity to praise God². Just as Hallel is recited with a beracha beforehand and a beracha afterward,³ so too pesukei d’zimra. This idea is made explicit by the Rif in his commentary on Masechet Berachot where he brings the sugya from Shabbat 118b.

רי”ף ברכות כ”ג א

וגרסינן בפרק כל כתבי הקדש [שבת קי”ח ב] אמר ר’ יוסי יהא חלקי עם גומרי הלל בכל יום …כי קא אמרינן בפסוקי דזמרה אמרינן…ותקינו רבנן למימר ברכה מקמייהו וברכה מבתרייהו. ומאי ניהו? ברוך שאמר וישתבח. הלכך מיבעי ליה לאיניש דלא לאשתעויי מכי מתחיל בברוך שאמר עד דמסיים [ליה] לשמונה עשרה 

Rif Berakhot 23a

And it is written in the chapter kol kitvei (Shabbat 118b): R. Yosi said, “May my portion be among those who complete Hallel every day”…When we make this statement, we are referring to pesukei d’zimra…And the Rabbis instituted that people recite a blessing before them and a blessing after them. And what are these blessings? Baruch she-Amar and Yishtabach. Therefore a person is forbidden from interrupting once they recite Baruch she-Amar.

The basic structure of pesukei d’zimra mirrors Hallel – an opening and closing beracha surrounding verses and chapters of praise⁴. Once this structure is in place, we have one way of approaching this unit of tefila. Hallel on Sukkot comes along with a certain type of joy. While that kind of overwhelming joy is not possible, and not appropriate, on a daily basis, we have some emotional direction when entering into pesukei d’zimra. Our starting place is that of joy. The idea that we are meant to approach God with joy is a powerful reminder of the nature of the relationship that many seek to cultivate with the Creator.

Beginning our day with joy is not always easy. The siddur is, in some ways, an emotional and spiritual roller coaster. As we will see though our study of pesukei d’zimra, even within this one section there are different – and sometimes competing – themes, values and ideas that we encounter along the way. Learning to become aware of our own internal experience and then working to direct those feelings towards God is not easy. I hope and pray that we are able to joyfully stand before the Creator of the World every day of our lives. The reality of the world in which we live is that such an aspiration may sometimes be impossible. It is perhaps this reason that R. Yosi introduces us to pesukei d’zimra with a plea to be blessed to complete these words with joy every day.

1. There is a major debate regarding which chapters are the centerpiece of pesukei d’zimra. For these essays, that question is not relevant as we are beginning our analysis from the outside and trying to develop broad themes.
2. The gemara says that anyone who recites the classic Hallel every day, known as הלל המצרי because it starts with בצאת ישראל ממצרים, is concerned to have engaged in blasphemy. One way to think about the different between הלל המצרי and פסוקי דזמרא is that the former thanks God for historical miracles while the latter recognizes God in nature. Praising God for nature is an appropriate daily practice, but we cannot always live in the moment of divine miracles as that might lead to blasphemy.
3. See Mishna Sukka 3:11, and the Gemara Sukka 39a there. See Shulchan Aruch, Orach Chayyim 422:2
4. This idea appears in several subsequent rishonim: see רא”ש ברכות פ”ה ס”ה, also שבולי הלקט ענין התפילה סימן ז. This language appears almost word for word in תורת המנחה of רבינו יעקב בר חננאל סקילי who was a student of the רשב”א and lived in the 14th century, see דרשה כב לפרשת בא ריש ״ביאור התפילה ״ברוך שאמר, עמ׳ 213 edited by הרב ברוך אביגדור חפץ. This is ultimately codified in טור in או״ח סימן נא.