Go through the two beginner platformer tutorials and all this is covered. Make your "components" or tiles a size that is divisible by 2 like 32x32 or 64x64. Turn on snap to grid and set your grid size to 32x32. Turn off pixel rounding.
Also make sure your characters animation frames don't have odd collision polygons. If you follow the beginners platformer tutorials they will also go over using a rectangular sprite as your collision polygon so that it doesn't change with each frame of animation.
THese should get you started. But the main piece to look at is the platformer tutorials. If you go to the tutorials section they should be in the top 5 that show up on the main page. Or you can just click the links below:
Building a Platformer - A beginners Guide
How to make a platform game