There are a number of conditions that will cause a wii to brick:
-Uninstalling the system menu or the IOS that runs the system menu = brick
-Installing a stub IOS instead of the IOS that is needed to run the system menu. For example, if you install IOS60 v6400 (a stub) instead of IOS60 v6174 and you are running System Menu 4.0 or 4.1, you'll brick.
-Installing a faulty wad can lead to a brick (commonly known as banner bricks)
-Installing the wrong IOS to run the System menu will lead to a brick. For instance, if you install IOS30 v1040 and System Menu 4.0 - 4.1 and you don't have IOS60 v6174, you'll brick because IOS30 is needed to run System Menu 3.2, but cannot be used to run any other version of the System Menu. However, if IOS60 v6174 is present on the wii, then you'll have no problems because IOS60 v6174 runs System Menu 4.0 - 4.1.
There are definitely other ways to brick (e.g. doing something stupid with preloader), but these are the most common ways that I could think of. If you look at the numerous "OMG I bricked mah wii!!1!" threads, you'll find that most of the bricks fall into the first 3 categories I mentioned. That being said, people need to read extensively so that you know what you're doing before you softmod, and relying on current, trusted guides (e.g. complete softmod guide or xzxero's guide) is the way to go.