Acestream (fork of the VLC player for video playback via torrents) was easy to install using apt-get on Ubuntu 14.04, but on Ubuntu 16.04 it is not in the repositories at the moment of writing (please let me know if it changes). One way is to install Acestream from source, but it could be difficult. The second way is was described here (Spanish, the link is dead already). I decided to gather all necessary files into an archive to make installation simpler.

To find out if your computer is running 32-bit or 64-bit version of Linux type uname -a in the terminal. If the output contains i686 or i386, then your Linux is 32-bit. If the output contains x86_64, then your Linux is 64-bit.
32-bit Linux

Download the appropriate archive: Acestream 32-bit.

Install the files as follows, using dpkg or gdebi:
user ~ $user ~ $unzip acestream-32.zip
cd acestream-32
root acestream-32 #root acestream-32 #root acestream-32 #root acestream-32 #root acestream-32 #dpkg -i 00-libgnutls-deb0-28_3.3.15-5ubuntu2_i386.deb
dpkg -i 01-acestream-engine_3.0.3-0.2_i386.deb
dpkg -i 02-acestream-player-compat_3.0.2-1.1_i386.deb
dpkg -i 03-acestream-player-data_3.0.2-1.1_i386.deb
dpkg -i 04-acestream-player_3.0.2-1.1_i386.deb

64-bit Linux

Download the appropriate archive: Acestream 64-bit.

Install the files as follows, using dpkg or gdebi:
user ~ $user ~ $unzip acestream-64.zip
cd acestream-64
root acestream-64 #root acestream-64 #root acestream-64 #root acestream-64 #root acestream-64 #dpkg -i 00-libgnutls-deb0-28_3.3.15-5ubuntu2_amd64.deb
dpkg -i 01-acestream-engine_3.0.5.1-0.2_amd64.deb
dpkg -i 02-acestream-player-compat_3.0.2-1.1_amd64.deb
dpkg -i 03-acestream-player-data_3.0.2-1.1_amd64.deb
dpkg -i 04-acestream-player_3.0.2-1.1_amd64.deb

Note
If you are running into the following issue: «trying to overwrite <filename> which is also in package <packagename>», you may want to add the flag —force-overwrite to your installation command. Attention: then the mentioned file will be overwritten and mentioned programs may fail.