You can move apps to the SD card using the applications menu (applications > downloaded, select app, select "move to sd"). This does not work for all apps (if the button is greyed-out the option isn't available for that app), and you should not move any app which has a widget that you use - if you do the widget will stop working. But as long as you are on Android 2.2 or later (and surely no Desire is still on 2.1?) you will have this option.
You can't move pre-installed system apps either, but those exist in a different storage partition so you wouldn't gain any space by moving them even if you could.
To do more than that will require rooting the phone, and probably installing a custom ROM. If you want to learn about that, follow the red link in my signature, which will take you to a post which collects information about rooting the Desire and what you can do then (e.g. the "root memory faq" describes options for expanding storage, either using a partitioned SD card or a custom hboot - the latter will only work with a custom ROM which does not include HTC's Sense software, the former is available with most custom ROMs).