Hi,
It's not an easy answer to 'speed up magento' - since every store is different / hosting etc..
In terms of magento out the box; ensure javascript and css merging are enabled in System > Developer > Merge CSS / JS
When merging JS - be sure to test your javascript after and ensure that it all still works; since some third party extensions don't always work with this enabled.
Also make sure that flat catalog is enabled too and that all your caches are enabled.
You can also run your page against Google Speed Test - fixing all the things it will flag up will be difficult though (e.g. moving javascript below the footer etc...) - this could be as simple as fixing things like image compression; using sprites instead of multiple images.
Then; there is your hosting - enabling things such as gzip compression and the like - however how to / if you can do this depends on what hosting you're on.
