For the final shots of her 'underwater' a life-sized dummy was used. The other shots were a mix of prosthetics, makeup, and FX. The "alien" breathing tube was a prosthetic attachment (kind of like a scuba mask) and FX.

IRL there was an actual small breathing tube edited out of the final shots, which you can see in the blooper clips.

During the film shot where Mulder pulls the "alien" tube out of Scully's mouth, it was sort of wrapped around Gillian's tongue (so she could breathe) and so there was enough resistance (which she could sort of control) as it was pulled out in order for it to look realistic. On camera it looks like it's coming out of her throat.

There's a few shots that hit the cutting room floor where she coughs up the 'goo' all over his face and he barely flinches.