Yes, the 300D supports E-TTL according to the specs
And it appears that the Promaster 7500DX is compatible with your camera, as long as you have the Canon version of the Flash. The manual says it works in TTL mode for older cameras, and E-TTL for later models.
The Canon version has the letters "CN" at the bottom of the back side of the flash, near the on/off button. You can see this in the user manual (PDF).
To use in TTL Mode
Set the flash to TTL mode, and the camera can be in Program, Manual, Aperture or Shutter priority modes. The camera should do all the work.
To use in Manual Mode
If you cannot get TTL to work, set camera ISO to 100, shutter speed to something under the sync limit, say 1/125th, set the flash to Manual, start at full power (1/1) and use the Guide Number from the manual.
So with a 50mm lens , full flash power (1/1) the guide number is 102 (ft). So if you subject is 10 feet away, 112 ÷ 10 = 11, so set the camera aperture to f/11. Or you can set the flash power to 1/4 power, guide number from the chart is 56, so now at 10 ft subject distance you would set the aperture to 56/10 = f/5.6
If you're unfamiliar with Guide Numbers, there is an explanation here: How can I calculate the effect of non-TTL flash on exposure