How is turning on lights on Shabbat considered work?
Without sacrifices how do we atone for our sins?
There is a widespread misconception that merely offering a sacrifices attained atonement for sin. As will become evident, this is not the true Jewish Torah-view.
The primary aspect of atonement was, and still is, Teshuvah: regretting and correcting (to the extent possible) the actual wrongdoing.
No matter the punishment or sacrifice, the sin is not atoned until the person first does Teshuvah: regreting his action, resolving never to repeat it, and confessing (i.e. asking forgiveness for) his sin before G-d. Only after these conditions are met, is the sacrifice accepted as an offering on the altar in the Temple, bringing an additional level of atonement.
That is why one who sins is commanded1 to repent and to confess his sin. Those who are required to bring a sacrifice for their sin, must also confess their sin at that time.2 The requirement of repentance and confession also applied to anyone who received punishment from a Jewish court of law (such as corporeal or capital punishment), as well as to any interpersonal sin, i.e. one committed by man against man (e.g. damaging a person or his property).
As far as attaining the added level of atonement attained through a sacrifice, see Is there any substitue for the animal offerings which brought atonement?
See also What is the Jewish approach to repentance?