Rule #1: Keep only one HUD in your inventory.
The reason for this is that the HUDs (particularly the ones with female components) are designed to operate even when they can't contact the back-end servers. If you attach an old HUD, it may try to upload its older state to the server and replace your current condition. For this reason, it's recommended that you immediately delete your old HUD once your new one is working. You'll save yourself a lot of grief, and keep your inventory that much cleaner. If you ever accidentally delete your HUD, you can just get a fresh copy from any in-world vendor -- it will automatically pull your state from the last backup.
Second, upgrades are not boxed. There is no need to unpack; just wear the new HUD. If you've kept your HUD in the default position (bottom center), you can just wear it immediately; most viewers will automatically detach your current HUD from that position (but you might want to check what you're wearing to confirm -- wearing two HUDs at once doesn't work well). If you've chosen a different position, just detach your current HUD and attach the new one at your chosen attachment point.
If you're in a sim where you can rez objects and you're currently wearing your HUD, you may also rez your HUD on the ground. It will request attach permission, then "jump" into place; see below (Upgrading a Locked HUD) for a description of how that works.
Once you've upgraded and confirmed everything's working properly, you should delete your old HUD and empty your trash. See Rule #1.
If your HUD is locked, it can't be detached, thus preventing upgrades simply by attaching a new HUD. If you have received an upgrade, you can rez it nearby (within 10m). If your HUD detects the new HUD and determines that it's a newer version, the new HUD will request attach permission. If you grant it, your current HUD will detach and the HUD you rezzed nearby will automatically attach to the same position as your old HUD. It will, of course, automatically lock after it downloads your configuration.
If you fail to respond affirmatively to the request for permission to attach, just take the new HUD back into your inventory, wait a few moments, then rez it again.
If you use outfits, you've likely saved your HUD as part of those outfits. Simply wearing an updated HUD won't update the outfits. That can cause you to accidentally wear an older HUD, which can cause problems (see Rule #1. Really... I'm serious about that). Fortunately, in Firestorm (and likely other viewers), this is easy.
First, after receiving your new HUD, open your inventory window and search to find your HUD. You might be able to get away with searching for just "Deciduan"
Next, right-click (or possibly control-click on a Mac) on the old version and select "Replace Links". The old version should be shown in the "Source" field, and the dialog box should indicate that it has found some inventory links.
Next, drag the new version from your inventory into the field named "Target".
Click "Start". Firestorm will quickly replace your HUD in all of your outfits.
Finally, provided you've worn your new HUD, go ahead and delete the old one, and empty your trash.