1. download latest .tar.xz package
2. open the downloaded archive and extract it.
3. go to the extracted folder via terminal: cd /path/to/tribler/src
4. Then install python dependencies: pip install -r requirements.txt
5. launch Tribler: /path/to/tribler/src/tribler.sh
6. possibly create program launch entry with exec line: /path/to/tribler/src/tribler.sh

How to update? Tribler likely has its settings in:
$ ls -A1 ~/.Tribler
7.9
crash-report.log
tribler-core-error.log
tribler-core-info.log
triblerd.lock
tribler-gui-error.log
tribler-gui-info.log
version_history.json

so possibly just repeat the process of installation, only overwrite the previous folder.