In many cases, the phone will prompt you to install the updated software automatically. However, you can also manually start the process by opening the 'SW update' application, which is found in the Applications folder. The phone will check for available updates and, if available, prompt you to install them.
Typically, firmware updates become available for different markets over the course of a few days. Operator variants (i.e. those devices customised by an operator) can take longer because, in most cases, operator approval is required before the update can be distributed.
Thanks to Arun for the tip.
A note on PR (Product Release) numbers
The E7's version 14.002 firmware is also known as PR 1.1. However this is not the same as the PR 1.1 release for the other Symbian^3 devices (N8, C7 and C6-01). For the current Symbian^3 devices, a more accurate way to determine the version of the software is to look at the firmware version.
Nokia counts PR number by assigning PR 1.0 to the first public release. Minor firmware updates will typically, but not always, update the minor number by 0.1 (e.g. PR 1.0 to PR 1.1). Major firmware updates will typically update the major number by one (e.g. PR 1.0 to PR 2.0).
In the case of the E7, its PR 1.0 release (firmware version 13.x) was equivalent to the N8's C7's and C6-01's PR 1.1 release (firmware version 13.x).