Running Don't Starve on non-Ubuntu linux distributions yields errors like these (and the game does not start):

./dontstarve: error while loading shared libraries: libcurl-gnutls.so.4: cannot open shared object file: No such file or directory

That occurs for multiple different libraries. The problem is that the game does not bundle all the required libraries in its game folder, but relies on shared libraries being installed. That shouldn't be the case, at least for tarballs that GOG offers, but unfortunately it is the case for Don't Starve.

The solution is to copy the required libraries to <Dont Starve folder>/game/dontstarve64/bin/lib64 (I assume you have 64bit operating system, otherwise replace the "64" references with "32" paths).

For my Fedora 21, the following libraries were missing:
libcurl-gnutls.so.4 -> libcurl-gnutls.so.4.2.0
libcurl-gnutls.so.4.2.0
libgcrypt.so.11 -> libgcrypt.so.11.7.0
libgcrypt.so.11.7.0
libgnutls.so.26 -> libgnutls.so.26.21.8
libgnutls.so.26.21.8
librtmp.so.0
libtasn1.so.3 -> libtasn1.so.3.1.12
libtasn1.so.3.1.12
(the shorter names are just symlinks to the longer names)

Where to find those libraries? You can find either find them in the Steam runtime folders, which usually are:
~/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/usr/lib/x86_64-linux-gnu/
~/.local/share/Steam/ubuntu12_32/steam-runtime/amd64/lib/x86_64-linux-gnu/

Or, you can download them from Ubuntu package repository, version 12.04. Here are the download links:
http://packages.ubuntu.com/precise/libcurl3-gnutls
http://packages.ubuntu.com/precise/libgcrypt11
http://packages.ubuntu.com/precise/libgnutls26
http://packages.ubuntu.com/precise/librtmp0
http://packages.ubuntu.com/precise/libtasn1-3
You download and extract it, extract data.tar.gz and find the library.

Once you have located the libraries, just copy them to the game folder as mentioned above. Now the game should work. If you're missing another library, use the same approach to locate it in Steam runtime or search for it in the Ubuntu package repository and download it.

Thanks kparal!

I've recently gotten fed up enough with windows after reading the windows 10 EULA that I've made the jump to Linux for all things. Fedora has always been my distro of choice - but I've not often used in in anger.

After adding the various libraries you mention in your post, I managed to get don't starve with sound, but a wonderful black screen. Running from the terminal I get a wonderful list of errors, where none of the textures would load.

If anyone is trying to get don't starve running on a stock install of fedora (I'm running 22), you'll also need some s3tc libraries. S3 texture compression is patented, and hence does not ship with fedora. The RPM fusion repositories carry various different software packages which fedora does not.

I can't link (first post) so please demangle the following for instuctions on how to add the repositories
http : / / rpmfusion . org / Configuration

Once the libraries are set up, you'll want to install "libtxc_dxtn" on a 64 bit system, or "libtxc_dxtn.i686" on a 32 bit system.

Thank you kparal.

Fedora 28, huge problems understanding how to make it work again after an update. Your guide made it happen!

Very happy boy.

:))