Most software projects can be made with relatively little effort 10 to 100 times faster than they are at the time they are first released. Under time-to-market pressure, it is both wise and effective to choose a solution that gets the job done simply and quickly, but less efficiently than some other solution. However, performance is a part of usability, and often it must eventually be considered more carefully.
The key to improving the performance of a very complicated system is to analyse it well enough to find the bottlenecks, or places where most of the resources are consumed. There is not much sense in optimizing a function that accounts for only 1% of the computation time. As a rule of thumb you should think carefully before doing anything unless you think it is going to make the system or a significant part of it at least twice as fast. There is usually a way to do this. Consider the test and quality assurance effort that your change will require. Each change brings a test burden with it, so it is much better to have a few big changes.
After you've made a two-fold improvement in something, you need to at least rethink and perhaps reanalyze to discover the next-most-expensive bottleneck in the system, and attack that to get another two-fold improvement.
Often, the bottlenecks in performance will be an example of counting cows by counting legs and dividing by four, instead of counting heads. For example, I've made errors such as failing to provide a relational database system with a proper index on a column I look up a lot, which probably made it at least 20 times slower. Other examples include doing unnecessary I/O in inner loops, leaving in debugging statements that are no longer needed, unnecessary memory allocation, and, in particular, inexpert use of libraries and other subsystems that are often poorly documented with respect to performance. This kind of improvement is sometimes called low-hanging fruit, meaning that it can be easily picked to provide some benefit.
What do you do when you start to run out of low-hanging fruit? Well, you can reach higher, or chop the tree down. You can continue making small improvements or you can seriously redesign a system or a subsystem. (This is a great opportunity to use your skills as a good programmer, not only in the new design but also in convincing your boss that this is a good idea.) However, before you argue for the redesign of a subsystem, you should ask yourself whether or not your proposal will make it five to ten time better.