Where can I look for announcements of tenure-track positions?
A quick Google Search of 


  X faculty position ads


turns up a rather lengthy list of position ads, but they also include the websites which those ads are posted on. You can then "fan out" from there. (It defaults to jobs within 200 miles of your location, so you'll want to change that setting to "any" to see all the jobs it can find.)

Additionally, the professional society for your discipline or another similar organization probably has some sort of "clearinghouse" site where such announcements are collected. For example, in my discipline (Chemical Engineering), an organization called CACHE offers a central posting site for such positions. In other countries, there may be regulations requiring the positions be advertised in specific locations as well.

And, of course, it's possible to ask your friends, mentors, and colleagues where to look for positions! Independence doesn't mean you have to go it completely alone!