The process is pretty simple, if tedious. Use the source button on the Wayback Machine copy to get the raw page. Be aware that the Machine's crawler doesn't always grab the source when it grabs the page, so make sure it's giving you a source from before the cut-off; and compare your finished page with the TVT page to make sure you haven't missed any important edits.
A lot of the style markup is the same and don't need changing. Mostly what you need to update is links. First do a search and replace on "{{" and "}}" and turn them into "[[" and "]]". Then go through and fix the Camel Case links. If you do that inside the wiki's editor with the link suggestions gadget turned on, it'll save you a fair amount of time. Ptitles will need you to check the TVT page as rendered to find the text they're supposed to be. Do a preview and check for redlinks -- these will mostly be page names where we changed the capitalization or added punctuation.
Spoiler markup has to be changed, from "[[spoiler:hidden text]]" to "{{spoiler|hidden text}}".
Convert text inside a hottip to a <ref></ref> markup.
Save the image(s) on the page directly from the Wayback Machine to your machine, and upload them if necessary. Then just replace the TVT image/caption markup with ours.
Most TVT indexes are now ATT categories, so all you need to do is change the container around the index name. Oh, and always add the "Banned on TV Tropes" category when restoring a censored page.
Oh, and while you're doing all that, it wouldn't hurt to fix any spelling and grammar errors you come across.
That should cover just about everything you should encounter on a typical page. Anything not covered here, you have editing experience -- you should be able to know how to code something here to get the same look there.