How do websites identify us by looking at the IP address? Does the IP address change each time we log on to a website?

Depends if your IP is static or dynamic. It is usually it is done with cookies, when you accept cookies through your browser's settings. Cookies are files that identify you to the sites you visited.

The IP address information is part of the header information from your browser.
This gives a load of information about your computer.
For example this is what mine displays as:

Quote:

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Mozilla/5.0 (Windows; U; Windows NT 5.1; en-GB; rv:1.8.1.11) Gecko/20071127 Firefox/2.0.0.11

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IP addresses are needed to route information to and from your computer. As said, browser cookies can track you. Your IP, your ISP and the time you were on the internet and law enforcement can find you

Your IP address fom your ISP is generally leased to you for a specific amount of tme unless you have a static IP address. You can use Find My IP Address - Lookup to fnd your current address.

Networks can track your computer by the MAC (Media Access Control) address of your network card. Everyone of them is generally unique. I'm not sure if this address is passed end to end.