Upon seeing this question, I took a look at the user tag, and it currently has 1366 unanswered questions, and 4326 total questions. Seeing as that's quite a lot, I thought I'd help with the burnination (am I correct in thinking the burnination is done by users?). However, I can't really tell when the burnination should start or when it's "approved"? I found this question, but there are no answers.
Before you start doing anything, put a little bit of thought into the request:
Does this tag even need to be burninated?
There are a lot of burninate-requests posted to various meta sites that are... To put it gently... A complete and utter waste of everyone's time. Some folks will seemingly post a request for any tag they come across that isn't interesting to them personally - and then try to justify it with some hand-waving about a lack of experts.
Here are the criteria I try to use when deciding whether or not to completely eliminate a tag from the system:
Does it describe the contents of the questions to which it is applied? and is it unambiguous?
Tags which fail these tests - commonly referred to as "meta tags" - are effectively meaningless, and can be actively harmful. You may have to do some research here: I've seen folks call tags "meta" when they were perfectly relevant and unambiguous, simply because the name-caller had no idea what the tag meant. Don't forget to update the tag wiki if you find it lacking...
Is the concept described even on-topic for the site?
This is kinda self-explanatory; Stack Overflow doesn't need a kittens tag, at least not until someone releases a hot new framework and names it "Kittens". All that a blatantly off-topic tag is gonna do is encourage blatantly off-topic questions, so removing it is good for everyone. Just be sure and do your homework: the last thing you want is to start removing tags only to be attacked by a bunch of angry kitten.js users.
Does the tag add any meaningful information to the post?
This covers a pretty big range of issues, from folks typing complete sentences into the tag entryfield causing useless tags to be applied, to folks just going overboard and applying once-reasonable tags to questions where it is only tangentially-relevant, to folks just finding two different terms for the same concept and using both of them. I'll usually start by looking at the "related tags" sidebar: there should be a few tags listed, but if any of them are synonyms then they should be merged; if that's not the case, then I'll start looking through questions to see how many of them are actually about the concept represented by the tag (which I should have a basic understanding of after step #1). If the tag is superfluous on the vast majority of questions where it is used, then it should go.
Note that it's also worth checking the number of followers at this stage, mostly as a sanity-check: if a bunch of people are using a given tag to find questions they're interested in, then just maybe you missed something important when evaluating its value in context... Which brings me to:
Does it mean the same thing in all common contexts?
This is related to #1, but can be a bit harder to identify because such tags will have very well-defined meanings but can be interpreted differently when different tags are applied. For instance, a tree can be a data-structure or a visualization. You may have to look through quite a few questions to identify this situation, and again the related tags sidebar is your friend. Be aware though, this need only be a death sentence when one meaning is not far and away more common than all others - if a tag is used correctly most of the time, then just fix the instances where it isn't.
If you're thinking that these criteria are gonna be pretty tedious to evaluate on a tag with thousands of questions in it, then you're absolutely right - which is why I'm pretty skeptical toward a lot of these requests on those rare occasions I take time to do it. If you're thinking that it's not worth the effort for tags that generally don't seem to be causing any problems, then you're sharper than half the folks throwing up these requests. If it looks like pointless busywork, it probably is pointless busywork...
But sometimes, it's not. Sometimes, tags get in the way, add confusion, start fights, take the place of better tags...
If you think this is the case, then raise the matter for discussion on meta. Share your research, as outlined above, making your case for burnination. Use the tags discussion, burninate-request - and include the tag name in the title. DO NOT try for a two-fer - one tag per discussion.
If, after discussion, there is widespread agreement that a tag really does need to be burned, then...
Start by cleaning up the edges
Bad tags are often harbingers of bad questions. So if you're about to remove a bad tag, start by removing the bad questions it collected: find closed questions and delete them, find downvoted questions and close them (if they warrant it), find poorly-written questions and re-write them (if they deserve it). You get the idea.
When a tag is merely ambiguous, sometimes it makes more sense to just replace it with another tag, or one of a number of other tags. This can be a quick way of turning a bad tag into a good one, or at least accomplishing something other than raw destruction when removing it.
This cleanup is easily the hardest, most time-consuming part of the process. Document your progress here on meta, so that others can see what you're up to and get involved - many hands make light work! And again, if you don't think it's worth doing then just drop it and move on to something else.
Once you're done closing / deleting / editing and retagging, you can finally start...
Now you're ready to actually remove the tag wholesale from a whole bunch of questions. Caveat: don't bother with this unless you have full editing rights. Seriously - it's just a waste of everyone's time, because at this stage all that's left is mindless retagging - and for every question you mindlessly retag, at least two other people with full editing rights will have to approve your edit. So if you haven't yet gotten full editing rights, consider your job done - go answer some questions & come back when you can edit without approval.
Now, even if you can edit without approval... You probably shouldn't bother if there are more than a few dozen questions. Even if you have a few other people involved, 50-100 is probably the most you should bother with unless you're down-right masochistic. For tags that involve large numbers of questions, just flag the burninate-request and leave a note for the moderators that the cleanup is done. They'll pass this along to someone like me, I'll verify that you didn't lie about the sanity-checking and cleanup, click a button, and it'll be like the tag never existed...