I have a Kindle Fire HD that I'd like to use as my character sheet for a Pathfinder game.
What's the best way to go about doing this?
there are three basic approaches...
Character Sheet Apps
Dedicated Android Apps
I can't vouch for any of the dedicated apps, but you can find a bunch on the play store.
I can say that the various app stores have different apps in this field.
Ernir points out that web apps seem to work just fine. Some of these will work with the standard Android Internet browser...
I've used two browsers on my tablet... the built in Internet, and Google's Chrome, and will note that the guts of a web app may not work...
the one character sheet I've used online I used relied upon flash... and will not work on my tablet. Individual mileage will vary based upon installed software.
PDF with Annotations
This works fairly well if you have an app that does markup well enough. (This works better on certain tablets than on others - the Galaxy Tabs do this really well, due to the stylus... it was a pain on my Acer.)
The reader I'm using supports both inked and typed annotations, and is free (with paid unlock for expanded features). Radaee PDF reader is what I'm using.
I used this mode also on my Sony PRS600 ebook device. Worked well there, too.
On the Sony, this mode did not modify the actual file, but created a separate file with the annotations. Radaee, however, saves the annotations within the PDF, so do keep a backup unmodified version.
File in your Office Suite
This is the most work, because you have to create the sheet in the first place as an editable file.
This also is the least visually pleasing option for many... it's usually text and only text.
On the other hand, it's a portable output - you can send the sheet if need be to someone else, and know that they're going to be able to read it, since the vast majority either save as RTF or as MS Word.
Things to remember
The Fire is just an Android tablet. Really. It's been customized a bit, but in all ways that matter, it's a low performance Android tablet.
Each tablet and phone has different compatibility issues... just because it runs for you on your fire doesn't mean it will work on your buddy's Nexus-7 or Acer A100.
Just because it doesn't officially run on your tablet doesn't mean it can't... Some apps work fine sideloaded even tho' they say they are not compatible with a given device.
Sideloading is risky - if you can't get the app via one of the legit stores, you risk virus versions if you get it elsewhere.