There are some excellent photos of simple water-lifting devices from around the world at Schioler's site here.
Here is a photo of an Archimedean screw in action; this from @Bristol
As the screw rotates clockwise, the water - always flowing downhill - is lifted. At the top of the screw (top right in the picture) the water channel has an open end and the water flows into the collecting bucket (here, since this is an interactive display, it flows through the pipe back into the reservoir whence the water came). See also discussion of the screw and the water screw in Specific subjects: Mechanics.
These were normally small scale: besides the archaeology, note Seneca's comment 'sometimes we take up water in our clasped hands and pressing our palms together squirt out the water the way a pump does'. This analogy would not have arisen if force pumps typically discharged water in quantity.
seems to be what Aristophanes is referring to in fr. 679, being used in a garden for irrigation, and called a
Refs and further reading: Seneca NQ 2.16.1; J Oleson Greek and Roman Mechanical Water-lifting devices Toronto 1984