A very good post on how a PHP framework can be build I found here. Everyone should be familiar with the basic principles described in the article, so don't hesitate to read it carefully.

If anybody still asks should we learn a framework, I recommend him to read the recent post of Ian P. Christian. Before you start, however there are no recommendation there about which framework you've to choose, but he gives a good examples and advices why there's no need to apply common design patters over and over again.