Auto to stick

Is it posible to change a new jetta auto for a stick transmission?

yes

Anything is possible, but it would seem to me to be more expensive than it's worth, and you'd be better off selling the automatic and buying a 5 speed. There are buyers and there are sellers, look around and compare.

You would almost need an entire 5 speed car to get all the bits and pieces off of...there are many differences, like the injection, fuel lines, coolant heaters, etc.

You would need an ECU from a 5 speed car.
You would also need to run all the hardware, trim and other stuff for the gearshift and clutch.

It is NOT worth the grief. Sell the car and get another if you want a 5 speed.

It isn't as easy to swap the A4 style cars from auto to manual as it was to do in the A2's and A1 cabrio they just need the trans and pretty much a pedal cluster. but you will need everything from the brake booster to get a 5th hydrulic line to the slave cylinder to the new computer to rid it of the automatic programs.

You don't need a different ECU. The ECU just needs a bit set in the ROM to change the MAP to a standard transmission. You do need a VAG-COM for this though.

The coolant heaters are a convinience and not necessity.

The transmission, clutch, clutch pedal and associated parts, linkage and of course the shifter assembly would be the biggest issue.

Check out SVTWEB's post in the Classified section. He's selling all hardware except the stick and linkage to the tranny for $1000+Shipping.

It'd be interresting to see if you get better mileage with the 11mm pump and .158 injectors. You get better atomization of the fuel and may see better than 42/48.