He ordered a huge block of dry ice (frozen carbon dioxide), to stand on and then hung himself. He knew it would sublime and leave no traces, so that people would be puzzled on how he managed to hang himself.
The puddle of liquid under himself is his own urine which came out after death.
He threw the rope over the rafters, jumped up, slipped the noose around his neck and hung himself. The puddle of liquid underneath him is his own urine because he realized at the last second that this was a very poor decision.
like luke said you cant get ice in jail... this is the best answer so far!
There is a second prisoner in the cell, sitting the floor leaned against the wall with a very sad expression in his face and cheeks wet from tears. The guards ask him what the heck happened and the prisoner explains his mate wanted to die and talked about suicide all the time and he never managed to talk him out of suicidal thoughts so he felt sorry for him. He loaded his mate onto his shoulders lifted him up so that he could put the loose around his neck. The poor man pushed away the other man's shoulders and hang himself. The prisoner realized what he had just done, began to cry and peed in his pants (which left a puddle on the floor), upon realizing that his mate is now dead and he would be accused of being guilty.
well at least medication and TV is standard in germany's jails too. (although, I mean 'medication' in a different, illegal sense. Authorities deny it but in fact they fail to prevent from drug trafficking.)