My clothier is in jail for some reason. I don't know why because he's a clothier and the only mandates my Baron makes are for Lay Pewter items.
You can find out by going to the justice section in the stocks menu.
1. Cages are bad, as dwarfs will often let prisoners starve or die of thirst for no good reason. Use chains instead (have to be made of metal ropes won't do for justice). If you do this you can simply make food and booze stockpiles next to them and the prisoner will eat/drink by himself.
2. Prisoners will only receive water, make sure you have a water source and enough buckets.
3. I'm not sure if prisoners can eat prepared meals, try butchering something, he might receive some raw meat.
4. Soldiers who have woodcutting/mining/hunting enabled will fail to equip their uniform. This will also make them fail to equip a backpack which they will need if they are set to carry rations (the default).
This will also cause them to randomly claim any and all food items in your fort without eating them. Disable these labor for all soldiers or set them to not carry rations, if you want them to carry rations make sure every soldier has a backpack equipped (they will do this automatically if you have enough backpacks and they wear any kind of body armor/upper body clothing).
5. If you deconstruct the cage you should be able to dump it once it has been moved back to your cage stockpile, which should free the dwarf. The prison sentence will be upgraded to a beating. Make sure your captain of the guard/sheriff is equipped with the worst quality training weapon you can make.