It's a tricky process and it fails almost as often as it succeeds. But it does work, and when it works it give you access to a lot more apps than the ones sold by B&N. (They don't have very many free ones in their app store.) Let me tell you how to do it.
First things first. You'll need to change a setting to allow for installing third party apps. So far as I can tell you can't actually do that without first trying to download an app because I think the setting is hidden from normal view.
There are a number of apps you could go get but here's one I know will work.
Go to Freeware Lovers and download the latest Aldiko app. When you try to install it you will be prompted to go change the setting. Do it.
Next click on the tiny icon in the bottom left corner of your Nook Touch screen. (It's your download queue.) Select Aldiko and install it again. Open it.
Now let me give you a way to find the apps. Aldiko and the other 3rd party apps won't show up with the ones from B&N, so you'll need to install a new home screen or launcher in order to find them again. But there is also a shortcut that will tide you over until you get that launcher.
Click on the "n", and select search. Type in the name of the apps you've installed. They will show up in the search. Click on them and you can run them. Open one.
Now go to the home screen, and then open the search again. Note that the app you searched for is listed. You can open it by clicking on it - no search required.
Update: You might also want to install a replacement home screen. I posted instructions over here.
Hit & Miss
I haven't been able to install all the apps I wanted, unfortunately. I have the Amazon Appstore installed, but the latest Kindle app did not work. Fortunately I was able to back track to a 1.x version. I then installed the latest version (from the Appstore) on top and it works.
I also wasn't able to install Angry Birds. But I have installed a number of other games and apps and I am slowly working my way through my Amazon Appstore account.
All in all, I'm pleased. I wasn't thrilled with how few free apps B&N carried and I am not going to buy apps a second time (or even a first time, for most of them). B&N has almost no free apps and that was one way that the Kindle Fire beat the Nook Tablet. Now that has changed.
Also, the ability to install 3rd party apps was one of the other ways that the KF beat the NT; now it's no longer true.
This has drastically changed my opinion of the Nook Tablet. I wasn't happy with it when I took it out of the box but now i can do so much more with it. This one trick has moved the NT from the Discard category to the Maybe category. That's how happy I am.