Neshomeh has made a very thorough page about editing that you can find here: http://ppc.wikia.com/wiki/Help:Editing
You can choose to edit in Rich Text or Source (which is a bit like html, but much simpler). I usually mix between the two.

You need to move your claimed fic to the claimed badfic page. http://ppc.wikia.com/wiki/Claimed_Badfic and remove it from the unclaimed page. One of the easiest ways to do this properly is to have both the two pages open at the same time and then cut it from one page and paste it onto the other. I recommend doing this in the Source to make sure that the links make it over.

The fic should be placed in the right category and alphabetically after title.

You then look at it in the Rich Text Editor (or in the Source if you used RTE to move the text) and compare it to the rest of the claims to make sure that it looks right.

After doing this you simply write 'claimed by Church' along with the date, somewhere after the title. You can make your name a link to your user profile, which is also recommended.

You write 'claimed a bad-fic' in the summary box.

Then you use preview to check that it looks okay (and because every time you use preview a wiki-angel gets its wings) and if there's nothing that needs editing, you publish.

Then you click on the links to check that they work. If they don't, or if something else is wrong, don't sweat it. You can just go back and edit it again, until you get it right, or ask for help.