Go to Extensions > Modules.
Usually there will be several modules assigned to the same module position (e.g. Position 7)
At the top of the module list are the column tabs, you can click on these to alter the ordering of the list. Click on the far left tab that has an arrow symbol. The color of the symbol should change to black, this means that ordering is now 'ACTIVE'
Scroll down the list until you find the module you would like to change.
To the left of the module title in the module list you will see a black arrow symbol.
Click on this arrow, the module row will change color to green, you can now drag the row up or down the list of the same position to place it where you want it to show on the front end.
Release the mouse button. The module will now adopt the new ordering position.
Reload the frontpage and check your work.
That's all there is to it.