There are several ways of tracking a user on the web.
- Cookies have already been mentioned in the other answer. Essentially they are small pieces of data that websites can store and read from your computer. Usually they generate a unique identifier for you and store it in a cookie.
- Every browser supplies a User Agent string with each request. This string has version information about your browser and your operating system in it. You can see your own user agent e.g. on http://user-agent-string.info/parse
- Whenever you make a request via the internet the other party will see your IP address. Nowadays it is very common to put several computers behind a router which means that all these people will have the same IP address. If you are working in a small office it is likely that you have this setup so all your machines will appear to servers on the internet with the same IP address.
- Most browser always send referer information along when you click a link. This contains the URL of the page on which you clicked the link. It allows e.g. website administrators to track how people are finding their content.
Which of these pieces of information Google is using is something that only a Google employee will be able to tell you. Depending on how much effort you want to put into it you can track someone without using cookies by only looking at the other data.
Depending on how afraid you are of being tracked you can take countermeasures: While most browsers do not natively support changing the user agent there are usually plugins to do this. The use of referers can also sometimes be deactivated in the browser. Your IP address can be masked by hiding behind a VPN or the TOR network.
Note, though, that depending on your surfing habits Google might still be able to track you using only the information which URLs you visited at what time (provided they get that from their advertisements which seems plausible). You probably exhibit unique behavior and as long as you don't browse completely atypical (e.g. never looking at more than one page of content per website, never looking at content-related pages etc.) it might still be possible to identify you.