I also found that the Kindle sometimes displayed the smartphone (mobile) version of certain websites and not the full version, which the Fire HD certainly handles well. Setting the "Requested website view" (found under Settings) from "Automatic" to "Desktop" will fix this in most cases.
Day 2. Getting productive
Email is on the top of my list when it comes to being productive on a tablet. Support for Microsoft Exchange makes it quite easy for me to get my business mail on the tablet: You'll find it under "Apps" and "Mail". Using the most common email providers requires no more than typing in username and password. Thankfully the Exchange client wants only the name of the Exchange server, username and password - that's it.
By default, the email client only syncs email traffic dating back a month. To get email that dates further back, go to "Settings", tap on your email account name, scroll down to "Store messages" and select the "Forever" option, which will sync all folders and all emails (make sure your Kindle Fire HD has the necessary space!).
Day 3. Improve battery life on the road
The first time I took my Kindle with me on a long train ride, it died after about a combined 6 hours of TV watching. Suffice it to say, I expected more. My iPad usually gives me 8-9 hours of viewing time. Here's what I did to boost battery life:
Brightness: Lowering the brightness setting to about 70% made a difference of about 45 minutes.
Bluetooth and Wifi: If you're not using a Bluetooth keyboard (or other BT peripheral), you might as well turn off Bluetooth. And when you're on the road, watching a movie or reading a book, there's not much sense in having the Wi-Fi chip and antenna constantly on. To turn them off, swipe from the top of the screen, tap on "Wireless" and turn off both Bluetooth and Wi-Fi. In my tests, this added another 45 minutes.
GPS: Turning off GPS also added a couple of minutes to overall runtime. To do this, fire up "Settings" and go to "Location-based Services" and select the "Off" modes for both "Enable Location-based Services" and "Location & Google Search" settings.
Email syncing: By default, Kindle's email app tries to update your inbox every 15 minutes. Each of these checks consumes a bit of battery power. Personally, I'd rather have the email app sync when I'm actually using the email app. (See Day 2 for more on email syncing.)
Overall, I got another 2 to 2.5 hours out of the device just by turning off some features I don't need when consuming content.