Troubleshooting-Gaggia-Twin-Steam-Cold

First make sure that there isn't any sort of flow issue by looking at the section of this article that discusses steam wand blockages.
Make sure the machine is set to steam mode, and that the indicator light has come on to indicate that the machine is heated for steam.
It is normal to have water come through the steam function for the first 5-10 seconds of steaming. This happens because the hot steam condenses back into water after it leave the boiler and come into contact with the room temperature steam valve and wand assemblies. For this reason you should do a process called purging. The Baby Twin is unique in that the machine forces you to purge it before it will allow you to steam. The video on the right shows the correct procedure for this.

Steaming on the Gaggia Baby Twin: Part Four

If the preceding steps have not resolved the issue then the steam thermostat will need to be replaced. Instructions for replacing the thermostat can be downloaded here.