The most important thing to keep in mind when applying to ANY school is that each one has deadlines. As with any application process, if you miss those deadlines, the chances of your child getting accepted decrease substantially, if not completely. The adage "First come, first serve" certainly applies here.
With Catholic high schools, the process is made easier by the fact that ALL Catholic secondary schools follow the same basic timeline. (To preview the 2013-2014 timeline, click here to open the pdf version or here to download the Word version.) By following this timeline, you will guarantee that your child's application is given primary consideration (though obviously NOT ensure acceptance). Otherwise, your child will most likely be placed on a waiting list.
If you'll notice on the timeline, Step 1 is to fill out the Admissions Application (click here for the pdf version and here for the Word version). If your child is coming from a Catholic school, you will simply need to fill out and submit the Admissions Application to your elementary school by the Wednesday deadline posted on the timeline (the school will handle the rest). Otherwise, you will have to submit the application, along with school records (transcripts from grades 5-8, standardized test results, and the first quarter report cards for your child's current grade) directly to the high school of choice by the Friday deadline (see timeline).
One more thing worth noting: Your high school of choice may want you to fill out and submit THEIR application as well (along with the Archdiocese one). To find out if this is necessary, simply call the high school and ask to speak with an admissions representative.