Download mode is for updating the phone's firmware.
Remove battery, plug in the usb cable to the phone, open ODIN on the computer (need usb drivers installed before hand) on the phone hold volume up and down then plug the phone into the computer. Your phone will say DOWNLOADING. This method works even if you run into problems and the phone refuses to boot properly.
Recovery mode is for installing Update.zip. The method is tricky but involves holding volume up/down and power, the phone will show ATT then go black. It will repeat that but after the second time it goes black let go of power.
If that doesnt work, android debug tools ADB reboot recovery will work even better.
Or root the phone and use Clockwork Rom manager to boot into recovery, just press the menu item.