Browsing different websites
At the moment, it is not advisable to browse two different websites at the same time when you don't want your activity to be linked. The Tor client can't tell which tab/window you are using for each request so might send requests for both sites over the same circuit. The exit node operator could then spot the correspondence.
Instead, you should browse one website at a time. When you've finished on one site you should click the "New Identity" button in the TorButton menu. This will close your existing tabs and then you can start your browsing with the second website. Any circuits which were used before you clicked "New Identity" will not be used after, so preventing an exit node from linking activities on the two websites.
Don't press "New Identity" too much though, because it increases load on the Tor network. Any circuit which was first used more than 10 minutes ago (unless changed by the
MaxCircuitDirtiness Tor option) will automatically be ineligible for new requests.
There are plans to improve the situation, by letting your Tor client know when two requests correspond to different browser tabs or go to different domain names. At the moment though you are safest just browsing one website at a time.
Running different applications
The situation is different if you are interested in preventing activity on different applications at the same time, as proposal 171 introduced features to allow activities carried out by one application to be isolated from activities carried out by another.
By default, requests to the Tor client's SOCKS port coming from different IP addresses are isolated, as are requests which have different SOCKS authentication information. So the easiest way to isolate two applications is to configure them to use the same SOCKS port but with different SOCKS usernames and passwords (what you use as the username and password doesn't matter, as long as each application has a different setting).
You can also configure how the Tor client isolates connections by setting isolation flags for your SocksPort, TransPort, DNSPort or NATDPort. See the description of
SOCKSPort in the Tor manual for the possible flags. Do bear in mind however that enabling more isolation will both increase load on the Tor network and lower your performance.