If you are interested in how the air interface and the lower levels of TETRA work, you should have a look at the http://tetra.osmocom.org/ website.
My contribution so far was to search for a suitable demodulator (TETRA uses PI/4-DQPSK) which I found at the OP25 project (the author of the demodulator is KA1RBI).
I also implemented some "proof of concept" code which allows decoding speech traffic and converting it to raw audio using the TETRA reference codec. Please note that this cannot be used to listen to encrypted TETRA traffic, it only works if no encryption is used.