Working out focusing issues can be frustrating there's various factors contribute to making an image sharp and isolating where the issue your having is occuring is the first step. I'm not familiar with your camera or canons in genral but the steps should be the same regardless.
The first step is to rule out any issues with the camera/lens combo...
Set your camera to af-s, place your camera on a flat surface, ideally on a solid a tripod and set up a static object to focus on, something with text is ideal so you can see clear edge definition. Set your lens to the widest apperture and your camera to live mode, it is slow but usually very accurate for focusing. Select the centre focus point line up your object and then let the camera focus on the object. You can try zooming in on your lcd and adjust the focus manually to confirm it is a focused as possible but af should be correct here. Take a photo and look at it, this is as sharp as your lens is capable of being wide open, if it is not sharp in the centre here the issue is your lens and your options are closing down the apperture until the image is sharp enough or replacing the lens.
Defocus the lens by rotating the manual ring fully to either side and repeat the first step but this time use the viewfinder to focus and take the same picture, if the photo is less sharp with the viewfinder then there is a problem between the lens and the af system, this is where af fine tuning would come in to play. If your body does not support af fine tuning your options are again stop down the lens until it acceptably sharp or replace the lens.
If the first two steps are sharp enough the next step is to trouble shoot your technique, take the camera off the tripod and hand hold the lens keep the camera in af-s and focus on the same object and take a photo. Compare the images to the stabalised photo if it is less sharp your technique is preventing sharp images, either practice staying more stable,
heres some ideas, or close down the apperture to give you more play in focus distance.
If the above was ok test the different focus modes and make sure there is no issues with them.
If the above tests are ok test the diferent focus points and make sure they are ok.
If the above are all ok with a flat 2d subject then we know your camera, lens and basic shooting technique are all fine and the issue then becomes applying it in real practice. Focus recompose is fine technique but depending on subject matter and technique it does not always work for very shallow dof, remember that focus dof is on a flat plane parallel with the sensor, when you move to recompose you need to move with the focal plane to stop any shift in focus. Practice with static objects first.
If you're shooting at very wide appertures with moving subjects and you moving to some extent as well using single servo there are always going to be a large risk of not nailing focus, using the right apperture and knowing what focus modes suit what circumstances will allow you to massively improve your keeper rate. Ultimately the best results will come through practicing and understanding the limits of you gear.