There are a couple of good ways to try and determine unique visitors, none of them are exact (which is why different analytics will report different numbers).
The first is to use a cookie. Create a cookie for the user for each time frame that you want to track uniques, so you could create one that expires in a day and one that expires in a month. You can then use both of those to track how many unique daily/monthly visitors you have. Of course this is not perfect since people can clear or refuse cookies, but it is pretty accurate.
The other way is to track uniques using a combination of the IP address and User Agent of the requesting user, this is probably slightly less accurate since if a company has a good IT group lots of internal users will have the same User Agent and since they are all coming from the same internal network could have the same IP address.
If you are interested in reading more about the different methods there is a great article about it here: http://www.google.com/support/urchin45/bin/answer.py?answer=28325