Hello.

The installation was very easy, but some people on this forum have asked
about it, so here are the steps:
1. Install/extract the game data from the GOG installer (worked fine with
wine)
2. Download the appropriate installer (TFE or TSE) from LIFG
2a. Run your installer from a terminal with

sh serious.sam.tfe_1.05beta3-english-2.run --keep --noexec

This extracts the installation data to a new folder
"serious.sam.tfe_1.05beta3-english-2" in the current directory.

3. Copy the binaries

cd serious.sam.tfe_1.05beta3-english-2
chmod +x bin/ssamtfe
tar xf bins.tar.bz2
cp -r bin/ssamtfe Bin/ YOUR_TFE_INSTALL_PATH/

3a. You may want to edit ssamtfe (it's a bash script) and change

GAME_BINARY="ssam_lnx"
to
GAME_BINARY="ssam_lnx.dynamic"

and uncomment
#SDL_AUDIODRIVER="alsa"

EDIT: Also, on line 116, change
cd ${GAMEDIR}
to
cd "${GAMEDIR}"

4. Run the game using YOUR_TFE_INSTALL_PATH/ssamtfe !

If you get really bad performance around torches/rockets, disable lens flare.

Hope that helps the linux players.