I would say that for the general tablet user, stick to applications you can find through http://www.gronmayer.com/n800/repos/ and install them through the application manager (as will happen if you click on the right places there. And after that visit you will have more applications to choose from in the application manager listing.) This is an almost 100% problem free way of installing applications.

If you really want to install something not already in a repository, then look for *_armel.deb files. They can be installed with the application manager too, but you may easily run into a problem where there are unmet dependencies, which means that you have to start hunting those down. Personally I only in rare cases bother with this, even though I'm very familiar with both Linux and the Debian package format.

If you can't find a .deb, in 99.9% of the cases you shouldn't go there. In particular, .tar.gz files are gzip-compressed tape archive files, and they almost always contain source code, not an installable application. Not what you want, unless you're a developer. The exception is certain special projects like Penguinbait's KDE environments, but in those cases there are good detailied instructions, and usually right there in the ITT thread where the project was announced.

Now please go read the first paragraph again..