To overpower the sun during the day you need either very high speed sync (i.e. with a leaf or electronic shutter), or tons of light and an ND filter.

The theory is that the exposure from a flash is practically unaffected by the shutter speed, so by using a high shutter speed you let in the same amount of flash but much less ambient light, allowing your flash to overpower the ambient.

The problem is, with most cameras, including your 20D you can't shoot past 1/250s when using the flash, as beyond that the second curtain starts closing before the first has fully opened and your flash is only visible in part of the image.

Some new flashes offer high speed sync, which pulses the flash to act like a continuous source. The problem with this approach is that when you up the shutter speed you let in less flash as well as less ambient so you don't gain anything. Some people combine several flashes to compensate for the loss of light, but in mist cases there's no difference between multiple flash HSS, and using tons of flashes with normal sync plus an ND filter. Here's a good post about using HSS to get the effect you want with multiple flash units: http://strobist.blogspot.com/2008/05/joe-mcnally-desert-shoot.html

Hit the comments for a lengthy debate on the merits of HSS vs. regular sync and ND filters (the short answer, you don't gain any extra power with pulsed HSS).

Older digital cameras used electronic shutters which don't suffer from the second curtain problem and so can sync up to 1/4000s without pulsing the flash, letting you overpower the sun with a single flash unit. See http://strobist.blogspot.com/2008/01/control-your-world-with-ultra-high-sync.html

edit:

With no extra gear, assuming you have a flash capable of HSS your only option is to get as close as possible with the strobe, light power squares with distance, meaning getting twice as close gives you 4 x the power, getting four times as close gives you 16 times the power! I would start at your base ISO, f/5.6 and walk the shutter speed up until you lose the ambient.