Sorry, I just read some of the manual on your ZyXel NSA310, and now I understand better. It is a 1-bay NAS on your network, and it has an eSATA port.
You can connect any SATA HDD to the eSATA port in one of two ways. Best is to mount it inside an external enclosure, as I said in previous post. However, you will not need to worry about installing a driver for the eSATA port - that's all done in the ZyXel for you. The alternative is to use an adapter to make your SATA HDD become an eSATA device, and you would need to have a power supply for the HDD as well - maybe it comes with the adapter. But then this HDD is bare - no protective case.
Once you connect the HDD to the eSATA port, you will have three options, it seems - see Section 8 of your manual starting on p. 161. You can have the NAS create a RAID1 array from the two drives for some data security. However, as MANY have said, RAID1 is NOT a good backup system at all! Or, you can have it expand the existing JBOD volume of the existing HDD to include the added HDD in a larger volume. WARNING: It is not clear to me right now whether doing this will wipe out all the data you already have on the internal NAS drive, or whether this operation preserves that data and merely adds the empty space of the second drive. Most certainly it WILL destroy the old data on the 250 GB unit you are adding.
The third option for this unit is that you can create on the added HDD a PC Compatible Volume, which just becomes a new separate drive available to the entire network. Doing this will certainly destroy old data on the added 250 GB unit, but the manual seems to indicate this will have no effect on the HDD already inside the NAS. See your manual, p. 166.