A Siddur, to simply explain, is a prayer book. During times of prayer, a Siddur is used. Jews do not read through the entire prayer book at every service. Depending on the service, is the part of the Siddur which is used.
For example, on Shabbat morning (Saturday), the Shabbat morning service is recited. This includes the Shema, the Amidah, the Torah or opening of the ark (Beit Hamikdash), ceremony, and the conclusion (Alaynu).
Many of the services share similar if not the same prayers. The Kaddesh is a prayer repeated throughout a service. It is said for anyone who is in mourning.
Depending on the synagogue service you attend, each temple uses a different Siddur. The Sim Shalom Siddur is common among many conservative shuls; it offers the option of adding in the matriarchs (women) of Judaism like Sara, Rachel, and Rebecca; and not just the patriarchs (Abraham, Isaac, and Jacob).
The nice thing about this Siddur is there are also English translations of all the prayers, as well as Hebrew transliteration for some of the important prayers for non-Hebrew readers.
At some synagogues, the Cantor will lead the service. In the temple I grew up in, our Cantor would play a guitar for Friday night services. The shock of many congregants that our Rabbi allowed this during Shabbat was another story but it was so unique and it made going to temple fun.