Do you mean Forum? Unfortunately, there is no official and/or pre-made way to "archive" Forum posts. They will be automatically converted to Discussion posts so if you are okay with Discussions and they don't need wikitext, you should be all set. If that solution is not satisfactory, then you need to find and implement your own alternative. The best alternative I have heard of so far is converting the content to fit wiki-style forums. However, the significant difference in structure means you will have to merge individual posts into a single page as opposed to keeping them separate like they currently are. I myself am exploring this possibility but it isn't looking so good for me since my wiki does have quite a few threads.
Article comments are not being moved at the same time as Forum. The reason is that the replacement feature is supposed to be separate from Discussions and is still in the design stage. The only thread-based discussion feature being removed in mid-January is Forum. Article comments, blog comments, and message walls will remain in place for now.
However, it is going to be removed at some point. Currently, the only alternative is to convert the content to talk pages. Doing this would be fairly similar to converting Forum to wiki-style forums.
There are different ways to have discussions on a Wikia wiki. There is (depending on what is enabled) live chat (/wiki/Special:Chat), Discussions/Community Feeds (/d), article comments, blog comments, message walls, Forum, DPLForum/wiki-style forums, and talk pages. Article comments, blog comments, message walls, and Forum are collectively referred to as threaded discussions because of how the data is structured. With threaded discussions, the wiki stores each comment as its own page. The page you are viewing with all of the comments is generated by retrieving the list of individual pages and then combining them into the format you see. This requires quite a bit behind the scenes which is one of the reasons why Wikia wants to get rid of them.
As with any other page, there is no "archive" option. You may see this mentioned here and there but all it really means is that the page is fully protected. In other words, only those with content moderator rights can make changes. When Wikia runs their script to remove Forum, that script will have content moderator rights. As such, "archived" pages will still be deleted.
The best you can do is preserve the content by transferring it somewhere else. To this end, Wikia's script will transfer all content to Discussions. However, Discussions is far from a perfect replacement for Forum. The biggest issue is that Discussions does not use wikitext. Therefore, any Forum post that uses wikitext will not be completely preserved and, upon editing the Discussions post, additional losses may occur. If this is an issue for your wiki (which it may not be) and you want to keep the wikitext versions, you will need to do your own separate content transfer. The most-similar feature to Forum is DPLForum. DPLForum is essentially talk pages in terms of how it works. Talk pages are essentially just regular pages except that the intended use is to hold a discussion.
Does that help clarify things? If not, what is still unclear?
As I said in my earlier post, there is currently no timeline for removing article comments. Even if there was, as I also previously said, the current options would involve a process more or less the same as what you need to use for Forum. The only difference would be that you are converting from article comments to talk pages rather than Forum to wiki-style forum. Both conversions, however, are more or less the same conversion of format; they just have different names.