I suspect that you just need a little practice.
But first just to be sure that you have not inadvertently set some option that is causing a problem, you should reset the camera to factory settings.
See page 100 of your camera manual to see how to reset the camera.
Now put the camera in Auto mode.
Place your hand on the camera is such a way that your four-finger is resting on the camera and use just the tip of your finger to press the shutter button.
Gently press the button half-way down.
To help, I suggest you look through the viewfinder and when the button is half-way down, the exposure settings under the image in the viewfinder will appear. That shows the settings the camera is going to use to take the picture.
Then while holding the button half-way down and still looking through the viewfinder, reframe your shot and press the button the rest of the way down.
The experienced photographer does this naturally just to see what settings the camera has chosen.
If he/she does not like the camera's choice, they can then switch to a manual setting and set the exposure to fit the situation.
I recently purchased a Canon XTi used. I don't know if the camera is working properly or not. I understand that the auto focus happens when the shutter button is depressed half way. Then the shutter is to release upon depressing the button the complete way. My camera seems to focus and then take the photo immediately after that. I am not given an opportunity to hold the focus, compose and then release the button in full before the photo is taken. Do you have any ideas for me?